MathCastle
Number TheorySuperchallengeFactors & Multiples

Factors & Multiples · Superchallenge problem

How many pairs of integers (a,b)(a, b) with 1≤a<b≤301 \le a < b \le 30 satisfy gcd⁡ ⁣(2a−1, 2b−1)=7\gcd\!\left(2^a - 1,\ 2^b - 1\right) = 7?