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guys,

From the solutions of the Pell's equation x*x-2*y*y=-1,

how can we prove that whenever y ends in digit 5, then 7 | x ?

-Mathslover

Perhaps I should clarify a bit,x*x-2*y*y=-1 has solution

x=1, 7, 41, 239, 1393, 8119, 47321, 275807,.....

y=1, 5, 29, 169, 985, 5741, 33461, 167305,...

and the general solution is (xn+yn*sqrt(2))=(1+sqrt(2))^(2*n+1)

Apart from induction,how can we prove whenever 5|y then 7|x ?

From the solutions of the Pell's equation x*x-2*y*y=-1,

how can we prove that whenever y ends in digit 5, then 7 | x ?

-Mathslover

Perhaps I should clarify a bit,x*x-2*y*y=-1 has solution

x=1, 7, 41, 239, 1393, 8119, 47321, 275807,.....

y=1, 5, 29, 169, 985, 5741, 33461, 167305,...

and the general solution is (xn+yn*sqrt(2))=(1+sqrt(2))^(2*n+1)

Apart from induction,how can we prove whenever 5|y then 7|x ?

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