Baltic Way 1992 · Problem 5

Number Theory

Given that $a^{2}+b^{2}+(a+b)^{2}=c^{2}+d^{2}+(c+d)^{2}$ , prove that $a^{4}+b^{4}+(a+b)^{4}=c^{4}+d^{4}+(c+d)^{4}$ .

When you’re ready

Review material becomes available with the next Daily.

Review

Divisibility and factorization

Solution

Solution:

Use the identity $\left(a^{2}+b^{2}+(a+b)^{2}\right)^{2}=2\left(a^{4}+b^{4}+(a+b)^{4}\right)$ .

Results from Baltic Way 1992

8 teams

Score distribution

All team scores