數學題 plz help

A² + B² = C²
A² + B² + 2AB > C² ........ (因2AB是正整數 > 0)
(A + B)² > C²
A + B > C
A + B - C > 0
若 A + B - C = 1 ,
則
(A + B)² = (C + 1)²
A² + B² + 2AB = C² + 2C + 1
2AB = 2C + 1 ................ (因 A² + B² = C²)
2AB = 2(A + B - 1) + 1
2(AB - A - B + 1) = 1
2( A(B - 1) - (B - 1) ) = 1
2( (A - 1) (B - 1) ) = 1
(A - 1) (B - 1) = 1/2
因 (A - 1) 及 (B - 1) 為整數 , (A - 1) (B - 1) 不可能是 1/2 , 茅盾!
故 A + B - C ≠ 1
又 3² + 4² = 5²
3 + 4 - 5 = 2
故 A + B - C 最小值為 2。