Challenges for the mathematically challenged?

[Allen]

@ johnb
I agree 100% with your assessment.. I find I'm using calculus only occasionally, but the number theory is fascinating, partly because it's so practical. ( e.g. Chinese Remainder Theorem).

For Calculator work, I think it's also very practical to study integer factorization- even for small numbers (e.g. less than 10**12) this can be very instructive, and all of these can be implemented in some fashion on a RPN Calculator.

• Primality Testing
• Generating Primes
• Pollard Rho Method
• Modular exponentiation
  

( previous forum post about similar algorithms )

A very approachable (undergrad accessible) book on the topic: Cryptanalysis of Number theoretic Ciphers

Here's some of the "low hanging fruit" from Project Euler:

5% Difficulty

• Multiples of 3 or 5
• Even Fibonacci numbers
• Largest prime factor
• Largest palindrome product
• Smallest multiple
• Sum square difference
• 10001st prime
• Largest product in a series
• Special Pythagorean triplet
• Summation of primes
• Largest product in a grid
• Highly divisible triangular number
• Large sum
• Longest Collatz sequence
• Lattice paths
• Power digit sum
• Number letter counts
• Maximum path sum I
• Counting Sundays
• Factorial digit sum
• Amicable numbers
• Names scores
• Non-abundant sums
• Lexicographic permutations
• 1000-digit Fibonacci number
• Reciprocal cycles
• Quadratic primes
• Number spiral diagonals
• Distinct powers
• Digit fifth powers
• Coin sums
• Pandigital products
• Digit cancelling fractions
• Digit factorials
• Circular primes
• Double-base palindromes
• Truncatable primes
• Pandigital multiples
• Integer right triangles
• Champernowne's constant
• Pandigital prime
• Coded triangle numbers
• Sub-string divisibility
• Pentagon numbers
• Triangular, pentagonal, and hexagonal
• Goldbach's other conjecture
• Distinct primes factors
• Self powers
• Prime permutations
• Consecutive prime sum
• Permuted multiples
• Combinatoric selections
• Lychrel numbers
• Powerful digit sum
• Square root convergents
• Spiral primes
• XOR decryption
• Powerful digit counts
• Maximum path sum II
• Passcode derivation
• Square digit chains
• Large non-Mersenne prime
• Concealed Square
• Inverse Digit Sum
• Powers of Two
• Eulercoin
• Number Splitting
• Concatenation Coincidence
  

10% Difficulty

• Poker hands
• Totient maximum
• Ordered fractions
• Counting summations
• Path sum: two ways
• Largest exponential
• Prime generating integers
• Harshad Numbers
• Under The Rainbow
• Divisors of Binomial Product
• Siegbert and Jo
• One Million Members
• Digit sum numbers
• Window into a Matrix
• Sum of Squares II
• Stealthy Numbers
• Dominating Numbers