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Prove that if a≡b mod n and c≡d mod n then a−c≡b−d mod n??
 one year ago
 one year ago
Prove that if a≡b mod n and c≡d mod n then a−c≡b−d mod n??
 one year ago
 one year ago

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A.Avinash_GouthamBest ResponseYou've already chosen the best response.0
u start like a=kn + b........
 one year ago

FoolForMathBest ResponseYou've already chosen the best response.3
\(a≡b \pmod n \implies a=n.k+b \) where \( k\in \mathbb{N} \) \(c≡d \pmod n \implies c=n.p+d \) where \( p\in \mathbb{N} \) \(ac = nk+bnpd = n(kp) +(bd)\), where \( (kp)\in \mathbb{N} \). Hence \((a−c)≡(b−d) \pmod n \) QED!
 one year ago

A.Avinash_GouthamBest ResponseYou've already chosen the best response.0
c= pn+d ac=n(kp)+bd :P......m late
 one year ago

FoolForMathBest ResponseYou've already chosen the best response.3
Similarly we can show that \( (a+c)≡(b+d) \pmod n \) and more generally \( (pa+qc)≡(pb+qd) \pmod n \)
 one year ago

Hollywood_chrissyBest ResponseYou've already chosen the best response.1
so basically we need to show that difference between a and c will be a multiple of n
 one year ago
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