$982451653^2$

This can not be done directly on a 8-digit 4 function inexpensive simple calculator. But, it can be done indirectly.

Do not use Wolfram/Alpha or Unix's bc or some other extended precision calculator. A Friden mechanical calculator can do it also; but that would be cheating also.

**
This section requires Javascript.
**

You are seeing this because something didn't load right. We suggest you, (a) try
refreshing the page, (b) enabling javascript if it is disabled on your browser and,
finally, (c)
loading the
non-javascript version of this page
. We're sorry about the hassle.

The Digital Root Test saves the day again!

We know that $982451653$ is congruent to $7 \mod 9$ . So $982451653^2$ is congruent to $49\mod 9$ , or $4\mod 9$ .

Checking all the answers, we find that only $\boxed{965211250482432409}$ is congruent to $4\mod 9$ .