SMO Senior · 7. Primes, divisors, perfect squares and integer equations
Factor into primes and count divisors, turn integer equations into products of factor pairs, use remainders of squares and factorials, and finish with bounds, squeezing and growth arguments.
Count and add divisors from a prime factorisation.
Solve integer equations by factoring into a product equal to a constant.
Use remainders (đồng dư) of squares and factorials to rule out cases.
Count solutions of linear equations in integers.
Combine bounds and case checks into complete proofs.