A large power, modular order

Compute 2100mod72^{100} \bmod 7 without evaluating 21002^{100} directly.

Show hints (2)+
  1. Find the smallest kk with 2k1(mod7)2^k\equiv 1\pmod 7.
  2. Reduce the exponent 100100 modulo that cycle length.

Answer

Reveal answer →

2

Want the full step-by-step worked solution? It's part of Premium - along with a worked solution for every question in the bank.

Asked at: Timed Mental-Math & Sequences, ETF Market-Making

Related questions