Let p be an odd prime and a,b,c be integers so that the integers a^{2023}+b^{2023}, b^{2024}+c^{2024}, a^{2025}+c^{2025} are divisible by p.
Prove that p divides each of a,b,c.
Proposed by Navilarekallu Tejaswi number theorymodular arithmeticDivisibility