Number Theory
Primes, remainders and bases: the hidden structure of the integers.
- 21Primes and FactorsreadyBreak numbers into primes, then count, add and multiply their divisors straight from the exponents.
0% - 22Divisibility & Legendre's FormulareadyTest divisibility from the digits alone, fill in missing digits, and count the factors of a prime inside a factorial without multiplying anything out.
0% - 23GCD & LCMreadyBuild GCDs and LCMs from prime exponents, shrink big pairs with the Euclidean algorithm, and use Bézout's identity to see exactly which totals two step sizes can reach.
0% - 24Modular ArithmeticreadyWork with remainders instead of huge numbers: wrap around a clock, spot digit cycles, and use Euler, Fermat, Wilson and the Chinese Remainder Theorem to tame enormous powers.
0% - 25Algebraic Number TheoryreadyTurn numbers into variables, then factor: difference of squares, sums and differences of cubes, Simon's trick and Sophie Germain crack contest number theory.
0% - 26Diophantine EquationsreadyEquations where only whole-number answers count: factor them, bound them, or take a mod to prove that no solution can exist.
0% - 27BasesreadyEvery base is a regrouping rule: expand a numeral into powers of its base, then solve for digits or take a mod to read off remainders.
0% - 28Miscellaneous Number TheoryreadyPalindromes, coin problems and a grab bag of number-theory tricks: pair numbers up, find the largest total two coins can't make, and spot patterns in digits and grids.
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