Properties of Numbers in Modulus

Very Hard Number And Operations Number Properties

Consider the following three integers:

$X = 4a + 1$, $Y = 4b + 1$, and $Z = 4c + 1$, where $a$, $b$, and $c$ are integers.

Which of the following statements is true regarding the integers $X$, $Y$, and $Z$?

All three integers are divisible by 4.

At least one of the integers is even.

All three integers leave a remainder of 1 when divided by 4.

Their sum is an even integer.

Their product is divisible by 4.

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