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Problem 1: Suppose d Z. Recall the definition of equivalence modulo d in class; for all a, b Z, ab (modd)iffd|(ba). Supposen,m,x,yZ,nx (modd)andmy (modd). Provethat
Problem 1: Suppose d Z. Recall the definition of equivalence modulo d in class; for all a, b Z, ab (modd)iffd|(ba). Supposen,m,x,yZ,nx (modd)andmy (modd). Provethat
n+mx+y (modd).
(Hint: to show this, use the definition; i.e. Show that d | (x + y) (n + m).)
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