Example of Connections

¥How can modular arithmetic help you figure out if 2346 is a perfect square?

¥How can modular arithmetic help you figure out if 99416 is a perfect square?

¥Explain how modular arithmetic helps you find out that *x*2 – 5*y* = 27 has no integer solutions.

¥For what integer values of *n*
does *n*3 = 9*k* +
7? How does modular arithmetic help find the
values?