IMC Key Stage 3 · 3. Remainders, last digits and sequences
Find last digits by cycles, compute with remainders (congruences), simplify sequences given by sums with telescoping, and follow recursive sequences modulo 10 until they repeat.
IMC Key Stage 3 – Selected topics
Find the last digit of a large power using the cycle of last digits.
Calculate with congruences and apply the divisibility tests for 9, 11 and 99.
Recognise periodic sequences and use the remainder of the position on division by the period.
Turn sums into recurrences, telescope products, and find periods of recursive sequences modulo 10.