SMO Open · 6. Divisibility, remainders and digits
Factor into consecutive integers, follow remainders around their cycles, count prime factors in factorials, and treat digits by place value.
Prove divisibility for all $n$ by factoring and find the largest such divisor.
Compute last digits and remainders of huge powers with congruences and cycles.
Count prime exponents and trailing zeros of factorials with Legendre's formula.
Solve digit problems by place value and construct numbers digit by digit in proofs.