Mod calculator

Powers, inverses and orders modulo

m

For checking your work after you’ve tried it yourself.

Step 1:
Pick a mode

Power, Inverse or Order.

a, then k or m as asked.

Compare, then open Do it by hand.

What it does.

Works with remainders. Power finds the remainder of

a^k

divided by

m

, even for huge

k

. Inverse finds

x

with

ax \equiv 1 \pmod m

. Order finds the smallest

d

with

a^d \equiv 1 \pmod m

When it helps.

Checking a remainder you found by repeated squaring, or an inverse before you use it.

What it won’t do.

It uses one modulus at a time and doesn't solve equations. Moduli go up to

10^{18}

Example.

2^{10} = 1024

, so

2^{10} \equiv 24 \pmod{1000}

Work out

a^{k} \bmod m

a

k

m

Spaces and commas are ignored. a can be negative.

Try