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Question

Find the smallest solution in positive integers of x214y2=1.

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Solution

x21=14y2
Now checking by putting y =1,2,3... untill we get solution
y=1;=>x2=15 not possible
y=2;=>x2=57 not possible
y=3;=>x2=127 not possible
y=4;=>x2=225=>x=15
Hence, smallest solution is (x,y)=(15,4).

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