You Could Count Them All.

How many pairs of integers (a,b)(a,b), where 0a<b1000\le a<b\le 100, satisfy (b2a2)2(mod5), \left( b^{2}-a^{2}\right) \equiv 2\pmod{5}, (b2a2)5(mod8)? \left( b^{2}-a^{2}\right) \equiv 5\pmod{8}?

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