Problem 1. For a positive integer N , let c₁ < c₂ < · · · < c_m be all the positive integers smaller than N that are coprime to N . Find all N ≥ 3 such that
gcd(N, ci + ci+1)̸ = 1
for all 1 ≤ i ≤ m − 1.
Here gcd(a, b) is the largest positive integer that divides both a and b. Integers a and b are coprime if gcd(a, b) = 1.