Residue tables

Squares, cubes and other powers mod

m

at a glance.

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

Step 1:
Choose m

Any modulus from 2 to 60.

Up to 12 columns.

See which remainders that power can and can't leave.

What it does.

Builds a table of

x^e \bmod m

for every

x

from 0 to

m - 1

, so you can see at a glance which remainders squares, cubes and higher powers leave.

When it helps.

Checking a fact like "squares leave remainder 0 or 1 mod 4" before you rely on it.

What it won’t do.

Moduli up to 60 and powers up to 12.

Example.

Squares mod 8 are only 0, 1 and 4.

Powers

x^{e}

mod

m

Modulus

m

(2 to 60)

Highest power (1 to 12)

Power

e

to study

Tap a column header in the table to study that power.

Try

Only x coprime to m