Maths Olympiad Daily Problems

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It is my humble request not to create a ruckus out of this question , please don't just guess and try to give solution with sound reasoning And no meme is intended in the serial number so please take it as a normal question

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Find the number of positive odd integers that cannot be written as a non-negative combination of 9, 15, and 25. For example, 7 cannot be written as a combination of these three numbers, but 39 can be written as the combination 9 + 2 · 15. What about the number of positive even integers that cannot be written as a combination of 9, 15, and 25? What if you repeat the process using the three numbers 9, 21, 49? Write down your observations. Are there other triplets for which your observations hold.

This one is really a good problem

(a²+2b)²+8b²=65 Find all integral solution This problem is very easy (not for everyone)give it a try 🙏🏻

This is a set of 3 good algebra problems and I would like you all to solve by abstract and elegant methods rather than old traditional methods,Brute force and unnecessary manipulation without any justification should be avoided and I will post the solution on 10th March , and the first solver of these questions will get something from me (obviously not money as I am unemployed but something valuable) , please do pay attention to the heading of the question they may serve as a hint for begginers. Enjoy 😜