Determine all pairs of integers A B such that mn uv mAn u

Determine all pairs of integers A, B such that (m,n) ? (u,v) ? m?An = u?Bv

is an equivalence relation on the set of all pairs of integers.

A =

B =

Solution

Determine all pairs of integers A, B such that (m,n) ? (u,v) ? m?An = u?Bv

is an equivalence relation on the set of all pairs of integers.

TO BE REFLEXIVE , WE SHALL HAVE ....M-AN=M-BN ....A=B

TO BE SYMMETRIC , WE SHALL HAVE ....M-AN=N-AM ....A = - 1 ..

SO A = B = - 1 ...................ANSWER

A = - 1

B = - 1

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