freshmans_nightmare. Number-theoretic conjecture related to primes congruent to 1 modulo 3. It is well known that if p is a prime such that p \equiv 1 \mod 3 and p^k divides a^2 + ab + b^2, then p^{2k+1} divides (a+b)^p - a^p - b^p. However, a conjecture posed by a reader of Kvant magazine suggests that there are no solutions for k > 2

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