SMO Open · 7. Primes, divisors, perfect squares and integer equations
Factorise, count divisors, turn equations into products, control squares and primes with remainders.
Count divisors from a prime factorisation and build numbers with a given divisor count.
Rewrite integer equations as factor × factor = constant and count every integer solution.
Decide when an expression is a perfect square using differences of squares, residues and trapping.
Use parity, small moduli and the pigeonhole principle to prove facts about primes.