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[數學,M1&M2] Junior Math



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回覆 5#  sealion 的帖子


Try reasoning with modulus.

回覆 引用 TOP

You may also prove that x is odd and y is even

回覆 引用 TOP

Solution for Part (a):

1001MOD3 = 2
Since for all real square n,
引用:
nMOD3 =/= 2


So (y^2)MOD3 = 0 will lead to (x^2)MOD3=2 which is contradiction.

So (y^2)MOD3 = 1 and (x^2)MOD3 = 0

Hence, x^2 must be odd
Since 1001 is odd, y^2 must be even.




回覆 引用 TOP

Solution to Part (b):

(x+y)(x-y) = 1001

Since 1001 = 7 x 11 x 13

You can exhaust all x and y then.

回覆 引用 TOP



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