Suppose we are given a set S of 50 distinct ordered pairs of integers (ai , bi). Does there exist two ordered pairs (aj , bj ) and (ak, bk) in S such that both (aj mod 7 ≡ ak mod 7) and (bj mod 7 ≡ bk mod 7)? Prove your answer.

Hey mate where is the graph

Idon't see any graph, however the graph of the function : f(x) = x²-2x+3 is a parabola: 1) open upward (since a> 0)2) it intersects y-axis in 3 (y=3)3) its axis of symmetry is x = +1 ( -b/2a)4) it's minimum is y = -2, so its vertex is (1,-2)5) it doesn't intersect the x-axis since discriminant < 0