(35S) Number Theory Library
06-26-2015, 02:58 PM (This post was last modified: 03-02-2018 07:47 PM by Gerald H.)
Post: #1
 Gerald H Senior Member Posts: 1,461 Joined: May 2014
(35S) Number Theory Library
Edit 2015-12-14: Changed line 343 of programme.
Edit: Corrected description of PPT.

A suite of number theory programmes - I've tried to include everything I find essential.

If you think something is missing please make suggestions.

Improvements very welcome.

Entry points:

A, B, MOD -> A+B mod MOD

SUB MOD 519
A, B, MOD -> A-B mod MOD

MULT MOD 525
A, B, MOD -> A*B mod MOD

DIV MOD 528
A, B, MOD -> A/B mod MOD

BEZO 208
A, B -> gcd(A,B), C, D where A*C+B*D=gcd((A,B)

FIBO 849
A -> FNUMBER

CRT 600
A, B, C, D -> E, B*D where E satisfies E mod B=A & E mod D=C, B & D co-prime.

PRIME? 148
A -> 0 OR 1 as A is composite or probably prime.

CORNACCHIA 531
A, PRIME -> [B,C] such that B^2+A*C^2=PRIME or 0 if there is no solution.

NEXT CORN 768
E, PRIME -> [B,C], A, B & C as above, A the smallest integer > E so above equation has a solution.

√MOD 420
A, B -> C, C=√A modulo B or 0 if no solution.

PELL 621
A, 1 or 0 -> [B,C,1 or -1] or 0.
For input A, 1 the B & C satisfy B^2-A*C^2=1;
for input A, 0 the B & C satisfy B^2-A*C^2=-1 & if no solution 0 is returned.

PWR MOD 035
A, B, MOD -> A^B mod MOD

INV MOD 237
A, MOD -> A^-1 mod MOD or 0 if no solution.

NEXT PRIME 161
A -> nextprime(A) if A positive, prevprime(A) if A negative.

PPT 301
A -> prime or 0 as A is a prime power or not.

#PQARTS 665
A, 0 or 1 -> B, for 0 B is number of integer partitions, for 1 the number of integer partitions in distinct parts.

KRONECKER 340
A, B -> 1 or -1 or 0, Kron(A/B)

RABIN? 571
A, B -> 0 or 1, 1 if A is a strong pseudo-prime base B, 0 if not.

SPLIT 565
COMPOSITE -> FACTOR

MODF CORNA 780
A, PRIME -> [B,C] such that B^2+A*C^2=4*PRIME or 0 if there is no solution.

NEXT M CORN 829
E, PRIME -> [B,C], A, B & C as above, A the smallest integer > E so above equation has a solution.

PFOR 575
A -> B, B an A-digit prime.

COMP# 581
A -> B*C, B & C are A-digit primes.

ALL FACS 590
COMPOSITE -> A, B where COMPOSITE= A*B. Pressing R/S then factorises A etc until 1 appears.

RANDOM# 000
No input, produces a random integer.
Code:
 1    LBL Z 2    12 3    10^x 4    RANDOM 5    * 6    IP 7    RTN 8    REGX 9    1,000,000 10    RMDR 11    STO Z 12    - 13    ENTER 14    x^2 15    RCL B 16    RMDR 17    x<>y 18    RCL*Z 19    RCL A 20    RMDR 21    ENTER 22    RCL- A 23    + 24    RCL A 25    RMDR 26    + 27    RCL B 28    RMDR 29    RCL Z 30    x^2 31    + 32    RCL A 33    RMDR 34    RTN 35    XEQ Z506 36    R↓ 37    STO M 38    R↓ 39    STO N 40    1►R 41    RCL M 42    x≠0? 43    GTO Z047 44    RCL R 45    RTN 46    RCL M 47    2 48    RMDR 49    x≠0? 50    GTO Z057 51    2 52    STO/ M 53    RCL N 54    XEQ Z008 55    STO N 56    GTO Z046 57    STO- M 58    RCL N 59    XEQ Z264 60    GTO Z041 61    XEQ Z506 62    -1►I 63    + 64    0 65    CLx 66    2 67    / 68    ISG I 69    IP 70    REGX 71    2 72    RMDR 73    x=0? 74    GTO Z065 75    R↓ 76    STO P 77    RTN 78    RCL P 79    XEQ Z037 80    1 81    x=y? 82    RTN 83    +/- 84    RCL+ A 85    x=y? 86    RTN 87    CLx 88    RCL I 89    x=0? 90    RTN 91    CLx 92    A-1 93    x<>y 94    XEQ Z008 95    x=y? 96    RTN 97    REGX-1 98    x=0? 99    RTN 100    R↓ 101    DSE I 102    GTO Z094 103    0 104    RTN 105    XEQ Z062 106    A-3 107    XEQ Z004 108    2 109    + 110    XEQ Z078 111    SGN 112    RCL A 113    x<>y 114    RTN 115    XEQ Z506 116    4 117    x>y? 118    RTN 119    CLx 120    2 121    RMDR 122    x=0? 123    RTN 124    SQRT(A) 125    FP 126    x=0? 127    RTN 128    LASTx 129    IP 130    199 131    x>y? 132    x<>y 133    1000 134    / 135    3.00002 136    + 137    STO I 138    RCL A 139    RCL I 140    IP 141    RMDR 142    x=0? 143    RTN 144    ISG I 145    GTO Z138 146    1►C 147    RTN 148    ABS 149    XEQ Z115 150    RCL A 151    x<>y 152    x=0? 153    RTN 154    CLx 155    47053 156    x<>y 157    x>=y? 158    GTO Z105 159    1 160    RTN 161    IP 162    RMDR(REGX,2)+REGX-1►T 163    2+T►T 164    XEQ Z148 165    x=0? 166    GTO Z163 167    R↓ 168    RTN 169    RMDR 170    LASTx 171    x<>y 172    x≠0? 173    GTO Z169 174    R↓ 175    ABS 176    RTN 177    CLx 178    RCL A 179    x<>y 180    x≠y? 181    RTN 182    C+1►C 183    1►U►V 184    IP(RAND*A) 185    STO X 186    XEQ Z008 187    RCL+ C 188    ENTER 189    RCL- X 190    RCL A 191    XEQ Z169 192    1 193    x≠y? 194    GTO Z177 195    R↓ 196    R↓ 197    DSE U 198    GTO Z186 199    2*V►V►U 200    R↓ 201    XEQ Z008 202    RCL+ C 203    DSE U 204    GTO Z201 205    V►U 206    R↓ 207    GTO Z185 208    STO G 209    1►E►F-1►C►D 210    R↓ 211    REGY 212    REGY 213    INT/ 214    +/- 215    ENTER 216    RCL* D 217    RCL+ E 218    x<> D 219    STO E 220    R↓ 221    ENTER 222    RCL* F 223    RCL+ C 224    x<> F 225    STO C 226    R↓ 227    REGY 228    * 229    REGZ 230    + 231    x≠0? 232    GTO Z211 233    R↓ 234    RCL E 235    RCL C 236    RTN 237    XEQ Z208 238    R↓ 239    REGY 240    * 241    REGY 242    ABS 243    1 244    - 245    x≠0? 246    GTO Z251 247    REGY 248    RCL G 249    RMDR 250    RTN 251    CLx 252    RTN 253    STO N 254    x<>y 255    STO R 256    R↓ 257    RCL A 258    XEQ Z237 259    x=0? 260    RTN 261    RCL R 262    STO R 263    x<>y 264    REGX 265    1,000,000 266    RMDR 267    STO C 268    - 269    STO D 270    RCL R 271    REGX 272    1,000,000 273    RMDR 274    STO Z 275    - 276    STO Y 277    RCL* D 278    RCL B 279    RMDR 280    RCL Y 281    RCL* C 282    RCL A 283    RMDR 284    + 285    RCL B 286    RMDR 287    RCL D 288    RCL* Z 289    RCL A 290    RMDR 291    + 292    RCL B 293    RMDR 294    RCL Z 295    RCL* C 296    + 297    RCL A 298    RMDR 299    STO R 300    RTN 301    STO F 302    STO H 303    SGN 304    STO E 305    RCL F 306    STO G 307    SGN 308    STO+ E 309    RCL E 310    RCL F 311    ENTER 312    XEQ Z035 313    RCL- E 314    RCL F 315    XEQ Z169 316    STO F 317    1 318    - 319    x=0? 320    GTO Z338 321    RCL F 322    XEQ Z148 323    x=0? 324    GTO Z305 325    R↓ 326    RCL G 327    ENTER 328    R↓ 329    REGY 330    / 331    1 332    x<y? 333    GTO Z328 334    x≠y? 335    CLx 336    REGX*REGZ 337    RCL H 338    x<>y 339    RTN 340    STO E 341    x<>y 342    STO C 343    2*(1►D) 344    RMDR 345    x<>y 346    x=0? 347    GTO Z414 348    LASTx 349    RMDR 350    + 351    x=0? 352    RTN 353    SGN 354    STO D 355    XEQ Z389 356    RCL C 357    x<> E 358    STO C 359    x>=0? 360    GTO Z367 361    ABS 362    STO C 363    RCL E 364    SGN 365    x<0? 366    STO* D 367    RCL E 368    x=0? 369    GTO Z414 370    XEQ Z389 371    RCL E 372    4 373    RMDR 374    RCL C 375    LASTx 376    RMDR 377    * 378    9 379    x=y? 380    -D►D 381    RCL E 382    ABS 383    ENTER 384    x<> C 385    x<>y 386    RMDR 387    STO E 388    GTO Z368 389    0 390    RCL E 391    2 392    RMDR 393    x≠0? 394    GTO Z400 395    2 396    STO/ E 397    REGZ 398    NOT 399    GTO Z390 400    R↓ 401    x=0? 402    RTN 403    RCL C 404    8 405    RMDR 406    4 407    - 408    ABS 409    1 410    x=y? 411    +/- 412    STO* D 413    RTN 414    ABS(C) 415    1 416    x≠y? 417    CLx 418    RCL* D 419    RTN 420    XEQ Z506 421    RMDR 422    SQRT(REGX) 423    FP 424    x≠0? 425    GTO Z428 426    LASTx 427    RTN 428    x<>y 429    STO F 430    RCL A 431    XEQ Z340 432    0 433    x≥y? 434    RTN 435    RMDR(A,4)-(1►I) 436    x=0? 437    GTO Z441 438    RCL F 439    (A+1)/4 440    GTO Z037 441    CLx 442    STO G 443    A-1 444    REGX 445    2 446    RMDR 447    x≠0? 448    GTO Z456 449    R↓ 450    LASTx 451    / 452    1 453    STO+ G 454    R↓ 455    GTO Z444 456    R↓ 457    STO H 458    1+I►I 459    RCL A 460    XEQ Z340 461    x>0? 462    GTO Z458 463    RCL I 464    RCL H 465    XEQ Z037 466    STO J 467    G►I 468    RCL F 469    (H-1)/2 470    XEQ Z037 471    STO E 472    RCL F 473    XEQ Z262 474    ENTER 475    x<> E 476    XEQ Z262 477    STO F 478    1 479    x=y? 480    GTO Z504 481    STO G 482    R↓ 483    XEQ Z008 484    1 485    x=y? 486    GTO Z490 487    STO+ G 488    R↓ 489    GTO Z483 490    RCL J 491    2^(I-G-1) 492    XEQ Z037 493    XEQ Z008 494    STO J 495    G►I 496    RCL E 497    RCL R 498    XEQ Z262 499    STO E 500    RCL F 501    RCL J 502    XEQ Z262 503    GTO Z477 504    RCL E 505    RTN 506    +/- 507    STO B 508    +/- 509    STO A 510    RTN 511    XEQ Z506 512    R↓ 513    RCL B 514    RMDR 515    + 516    RCL A 517    RMDR 518    RTN 519    XEQ Z506 520    R↓ 521    - 522    RCL A 523    RMDR 524    RTN 525    XEQ Z506 526    R↓ 527    GTO Z262 528    XEQ Z506 529    R↓ 530    GTO Z253 531    XEQ Z506 532    √x 533    IP 534    STO K 535    R↓ 536    STO L 537    +/- 538    RCL A 539    XEQ Z421 540    x=0? 541    RTN 542    RCL A 543    x<>y 544    REGY-REGX 545    x>y? 546    x<>y 547    R↓ 548    RCL K 549    x>=y? 550    GTO Z556 551    R↓ 552    x<>y 553    REGY 554    RMDR 555    GTO Z548 556    R↓ 557    SQRT((A-SQ(REGX))/L) 558    FP 559    x≠0? 560    GTO Z563 561    [REGY,LASTx] 562    RTN 563    CLx 564    RTN 565    XEQ Z115 566    x≠0? 567    GTO Z183 568    RCL A 569    LASTx 570    RTN 571    x<>y 572    XEQ Z061 573    x<>y 574    GTO Z110 575    XEQ Z003 576    999,999,999,989 577    x<=y? 578    RTN 579    R↓ 580    GTO Z162   (corrected, was erroneously Z163, 2018-03-02) 581    6 582    x>y? 583    x<>y 584    STO G 585    XEQ Z575 586    x<> G 587    XEQ Z575 588    RCL* G 589    RTN 590    XEQ Z148 591    x≠0? 592    RTN 593    R↓ 594    XEQ Z565 595    / 596    LASTx 597    STOP 598    R↓ 599    GTO Z590 600    STO O 601    R↓ 602    STO N 603    R↓ 604    STO M 605    R↓ 606    STO L 607    CLx 608    RCL M 609    XEQ Z208 610    RCL* N 611    RCL* M 612    x<>y 613    RCL* L 614    RCL* O 615    + 616    RCL M 617    RCL* O 618    RMDR 619    LASTx 620    RTN 621    STO K 622    1►F 623    (REGZ►A-SQ(IP(SQRT(A))►B►D►H))►I 624    x=0? 625    RTN 626    IDIV(2*B,I)►C►G*B+1►E 627    RCL I 628    1 629    x≠y? 630    GTO Z637 631    RCL K 632    x>0? 633    GTO Z662 634    RCL A 635    [D,F,-1] 636    RTN 637    0►J 638    NOT(J)►J 639    IP((A-SQ((C*I-H)►H))/I)►I 640    1 641    x≠y? 642    GTO Z655 643    RCL K 644    x<0? 645    GTO Z650 646    RCL J 647    x≠0? 648    GTO Z662 649    GTO Z655 650    RCL J 651    x=0? 652    GTO Z662 653    0 654    RTN 655    IDIV(B+H,I)►C*E+D 656    x<>E 657    STO D 658    C*G+F 659    x<>G 660    STO F 661    GTO Z638 662    RCL A 663    [E,G,K] 664    RTN 665    x≠0? 666    GTO Z669 667    CF 0 668    GTO Z670 669    SF 0 670    RAD 671    2*REGY►K/2 672    24 673    1/x 674    FS? 0 675    +/- 676    - 677    STO G 678    FS? 0 679    GTO Z681 680    π*√(2/3)/G►I*(G^1.5►J) ►H 681    CLx 682    STO B 683    1►C 684     C►D 685    CLx 686    STO E 687    RCL C 688    RCL D 689    RMDR 690    LASTx 691    x<>y 692    x≠0? 693    GTO Z689 694    1 695    + 696    x≠y? 697    GTO Z721 698    +/- 699    RCL+ C 700    x=0? 701    GTO Z713 702    STO F 703    0 704    F/C 705    FP(REGX*D)-0.5 706    x<>y 707    0.5 708    - 709    * 710    + 711    DSE F 712    GTO Z704 713    0.25 714    + 715    K*D/C 716    - 717    π 718    * 719    COS 720    STO+ E 721    DSE D 722    GTO Z687 723    FS? 0 724    GTO Z737 725    EXP(H/C) 726    ENTER 727    1/x 728    (REGY+REGX)*I/C 729    (REGZ-REGY)/J 730    - 731    C+1►C-1 732    √x 733    * 734    π 735    4 736    GTO Z761 737    SQ(π/C)►L*G/12►D 738    SGN 739    ENTER 740    STO F 741    ENTER 742    R↓ 743    x<> y 744    RCL* D 745    RCL/ F 746    RCL F 747    1 748    + 749    STO F 750    / 751    + 752    LASTx 753    x<>y 754    REGZ 755    x≠y? 756    GTO Z742 757    RCL* L 758    2 759    STO+ C 760    6 761    * 762    / 763    IP(REGX*E+B►B+0.5) 764    IP(REGY+B+0.5) 765    x≠y? 766    GTO Z684 767    RTN 768    XEQ Z506 769    R↓ 770    STO U 771    RMDR(1+U,A)►U 772    RCL A 773    XEQ Z532 774    ABS 775    x=0? 776    GTO Z771 777    LASTx 778    RCL U 779    RTN 780    XEQ Z506 781    x<>y 782    +/- 783    x<>y 784    2 785    x≠y 786    GTO Z793 787    √(8+REGZ) 788    FP 789    x≠0? 790    GTO Z827 791    [LASTx,1] 792    RTN 793    R↓ 794    x<>y 795    STO K 796    x<>y 797    XEQ Z421 798    x=0? 799    RTN 800    RMDR(REGX+K,2) 801    x=0? 802    GTO Z808 803    R↓ 804    RCL A 805    x<>y 806    - 807    GTO Z809 808    R↓ 809    2*A 810    x<>y 811    IP(2*SQRT(A)) 812    x≥y? 813    GTO Z820 814    R↓ 815    RMDR 816    LASTx 817    x<>y 818    R↑ 819    GTO Z812 820    R↓ 821    SQRT(ABS((4*A-SQ(REGX))/K)) 822    FP 823    x≠0? 824    GTO Z827 825    [REGY,LASTx] 826    RTN 827    0 828    RTN 829    XEQ Z506 830    R↓ 831    STO L 832    3-RMDR(L,4) 833    1 834    x<y? 835    x<>y 836    RCL+ L 837    4 838    RCL* A 839    RMDR 840    STO L 841    RCL A 842    XEQ Z781 843    ABS 844    x=0? 845    GTO Z832 846    LASTx 847    RCL L 848    RTN 849    IP(((1+√5)/2)^REGX/√5+.4)-IDIV(REGX,56)-2*(IDIV(REGX,58)+ IDIV(REGX,59)) 850    RTN
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 Messages In This Thread (35S) Number Theory Library - Gerald H - 06-26-2015 02:58 PM RE: (35S) Number Theory Library - Gerald H - 03-02-2018, 10:37 AM RE: (35S) Number Theory Library - fred_76 - 02-13-2019, 04:41 PM RE: (35S) Number Theory Library - Gerald H - 02-15-2019, 05:34 AM RE: (35S) Number Theory Library - Dieter - 02-16-2019, 05:05 PM RE: (35S) Number Theory Library - Gerald H - 02-16-2019, 06:49 PM RE: (35S) Number Theory Library - Gerald H - 02-17-2019, 05:51 AM

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