Question

求x^2-y^2=1979的整数解

Answer 1

x^2-y^2 = 1979

(x+y)(x-y) = 1979

因1979是质数,所以

当 x+y = 1979 ,x-y = 1 时,x=990 ,y=989

当 x+y = 1 ,x-y = 1979 时,x=990 ,y=-989

当 x+y = -1979 ,x-y = -1 时,x=-990 ,y=-989

当 x+y = -1 ,x-y = -1979 时,x=-990 ,y=989