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Here's question I'm really struggling with:

enter image description here

So far I believe I have found $d=21$ and $x=-2$ and $y=5$.

From here I'm unsure where to go as part b is making very little sense, could someone explain a way to go about it?

I have used standard trial and error to find more pairs of integers that satisfy the identity as it asked in b(i), however I wonder if there is a mathematical solution.

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  • $\begingroup$ Welcome to MSE. It is in your best interest that you type your questions (using MathJax) instead of posting links to pictures. $\endgroup$ – José Carlos Santos Nov 10 '18 at 11:25
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What you did for part a is correct.

Now, part b is just to prove that the numbers $-2+105k$ and $5-252k$ are also solutions, for each $k\in\mathbb N$. And whoever created the problem asked you to prove this assertion by induction (a silly idea, in my humble opinion).

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