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# Modular Arithmetic Operations

Considering the remainder "modulo" an integer is a powerful, foundational tool in Number Theory. You already use in clocks and work modulo 12.

**True or False?**

The sum of two odd numbers is odd.

**True or False?**

The sum of the squares of any three odd numbers is odd.

**True or False?**

The sum of the squares of three consecutive integers is always odd.

Determine the parity of

\[ \large 101010_3, \]

that is, 101010 in base 3.

**Note**: In the context of number theory, the *parity* of a number is whether or not it is even or odd. This is different from the context of computer science, in which a parity bit counts the number of 1s in a binary code.

**True or False:**

The sum of an odd number and an even number is odd.

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