Prove that if a -= b(mod n) and c -= d(mod n), then if a-c -= b-d(mod n)

glasskerfu

glasskerfu

Answered question

2021-02-24

Prove that if ab(modn)andcd(modn), then if acbd(modn)

Answer & Explanation

Ayesha Gomez

Ayesha Gomez

Skilled2021-02-25Added 104 answers

The concept of congruence states that there are integers s and t that are
a-b = sn...(1) 
and 
c-d=tn...(2) 
(1)-(2) 
(a-b)-(c-d)=sn-tn 
(a-b)-(c-d)=n(s-t) 
Both s and t are integers so s−t is also integer 
put s−t=u 
(a-b)-(c-d)=nu 
By defination of Congruence 
(ab)(cd)(modn) 
Hence Proved, 
(ac)(cd)(modn)

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