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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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