SMO Junior · 7. Primes, divisors, perfect squares and integer equations
Factor into primes, count divisors, use the difference of squares, turn equations into products, and squeeze or use parity when factoring fails.
Count divisors, square divisors and cube conditions from a prime factorisation.
Solve problems where two expressions are perfect squares.
Solve integer equations by factoring and listing divisor pairs.
Use squeezing, last digits, remainders and parity of primes in proofs.