Question

Tìm số nguyên x;y biết :

      5xy + x + y = 4

Answer 1

Ta có : 5xy + x + y = 4

=> 5(5xy + x + y) = 5 . 4

=> 25xy + 5x + 5y = 20

=> (25xy + 5x) + 5y + 1 = 20 + 1

=> 5x(5y + 1) + (5y + 1) = 21

=> (5x + 1)(5y + 1) = 21

=> 5x + 1;5y + 1 ∈ Ư(21) ∈ {-21;-7;-3;-1;1;3;7;21}

Mà 5x + 1;5y + 1 chia 5 dư  1

=> 5x + 1;5y + 1 ∈ {1;21}

=>(5x + 1;5y + 1) ∈ {(1;21);(21;1)}

=> (x;y) ∈ {(0;4);(4;0)}