SMO Senior · 6. Divisibility, remainders and digits
Work with remainders instead of huge numbers: cycles for last digits, congruences, gcd by elimination, and digit sums modulo 9.
Find last digits of large powers with cycles of remainders.
Compute remainders with congruences, Fermat and Euler, and by splitting the modulus.
Use linear combinations, Euclid's algorithm and Legendre's formula for divisibility questions.
Solve digit and digit-sum problems with place value, modulo 9 and size bounds, including a Round 2 proof.