If a \equiv b (mod m) and c \equiv d

SchachtN

SchachtN

Answered question

2021-08-15

If kab (mod m) and cd (mod m), prove that acbd (mod m)

Answer & Explanation

ottcomn

ottcomn

Skilled2021-08-16Added 97 answers

Proof:
a=b+qm
c=d+rm, some r,q
acdb=(b+qm)(d+rm)bd
=bd+brm+qmd+arm2bd
m(br+qd+qrm)
Divisible by m, so acbd (mod m)

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