Fermat mentioned the given question repeatedly in letters. Assume we are given whole number N which is not a square. Can we find the square such that when we multiply N and add 1, result is also square?
i) Assume N = 2. Check that 4 is solution to Fermat's question. Can you find others?
ii) Find the solution for N = 3? For N = 5?
iii) For N = 7, one solution is 9 as 7 x 9 + 1 = 64 = 82. But there are many more. Find another one? Find the way to generate as many as you like?
iv) Find the solution for N = 61?