large modular arithmetic without powers

Question

How would you find the answer to this

$$111453 \cdot 1812337 \bmod(10)$$

I know how to do it if given powers but don't know how to solve something like this above.

Use the Congruence Product Rule $\ \ $ – Bill Dubuque May 11 '16 at 17:51 — Bill Dubuque, May 11 '16 at 17:51

score 2 · Accepted Answer · answered May 11 '16 at 16:46

2

Note : $$111453 \equiv 3 \pmod{10} \ and \ 1812337 \equiv 7 \pmod{10}$$ $$\implies 111453 \times 1812337 \equiv 3 \times 7 \equiv 21 \equiv 1 \pmod{10}$$

answered May 11 '16 at 16:46

C.S.

5,528

score 0 · Answer 2 · answered May 11 '16 at 16:47

0

It is equal to:

$111453$ (mod 10) $×1812337$ (mod 10)

answered May 11 '16 at 16:47

N.S.JOHN

1,549

1

And take mod 10 again if it gives a two digit number. – N.S.JOHN May 11 '16 at 16:49

large modular arithmetic without powers

2 Answers2