Is it a valid step while solving modular arithmetic equation?

Question

It's probably a very basic question. Is this equation $$91x\equiv21\pmod{56}$$ equivalent to $$35x\equiv21\pmod{56}$$ If so, then what property says that these equations are equivalent?

score 3 · Accepted Answer · answered Mar 20 '13 at 22:23

3

Yes, they are the same. You can write $91x=56x+35x$. Now since $56$ is zero mod $56$, this gives you that $91x=35x$.

Two numbers are the same modulo $56$ if their difference is an integer multiple of $56$.

answered Mar 20 '13 at 22:23

Lepidopterist

2,751

score 1 · Answer 2 · answered Mar 20 '13 at 22:39

1

Since we have $$ 91\equiv35\pmod{56}\quad\Rightarrow\quad91x\equiv35x\pmod{56} $$ this seems to be simply a Property of Equality or Equivalence.

answered Mar 20 '13 at 22:39

robjohn

345,667

Is it a valid step while solving modular arithmetic equation?

2 Answers2