Răspuns:
(a,b) ∈ {(14,336); (42,112); (112,42); (336,14)}
Explicație pas cu pas:
(a,b) = 14
[a,b] = 336
a = 14×m, b = 14×n, (m,n) = 1
a×b = (a,b) × [a,b] = 14 × 336 = 4704
14×m×14×n = 4704
m×n = 24
24 = 1×24 = 2×12 = 3×8 = 4×6 = 6×4 = 8×3 = 12×2 = 24×1
dar (m,n) = 1 => 24 = 1×24 = 3×8 = 8×3 = 24×1
m = 1, n = 24, a = 14, b = 336
m = 3, n = 8, a = 42, b = 112
m = 8, n = 3, a = 112, b = 42
m = 24, n = 1, a = 336, b = 14
=> (a,b) ∈ {(14,336); (42,112); (112,42); (336,14)}
