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It leaves a remainder of 1 when divided by 2. Or, if the number is n, then n-1 or n+1 is even (divisible by 2).

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It ends in 1, 3, 5, 7 or 9.

Q: How do you prove that an integer is an odd integer?

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The sum of an odd and an even number is odd. Any odd number can be expressed as 2n + 1 (for some integer "n"). Any even number can be expressed as 2m (for another integer, "m"). The sum of the two is 2(m+n) + 1. Since the expression in parentheses is an integer, multiplying it by 2 gives you an even number. Adding 1 makes the entire expression odd.

The next odd integer after 40 is 41

The number 71 is an integer, an odd integer, a positive odd integer, and also a prime number.

It is quite easy to prove this using algebra. Suppose x is the smaller of the two odd integer. The fact that x is odd means that it is of the form 2m + 1 where m is an integer. [m integer => 2m is an even integer => 2m + 1 is odd] The next odd integer will be x + 2, which is (2m + 1) + 2 = 2m + 3 The sum of these two consecutive odd integers is, therefore, 2m + 1 + 2m + 3 = 4m + 4 = 4(m + 1) Since m is an integer, m+1 is an integer and so 4(m + 1) represents a factorisation of the answer which implies that 4 is a factor of the sum. In other words, the sum is a multiple of 4.

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The statement is not true. Disprove by counter-example: 3 is an integer and 5 is an integer, their product is 15 which is odd.

It cannot be done. The basic rules of math. odd integer plus odd integer = even integer. odd integer plus even integer = odd integer. Always. odd integer plus odd integer plus odd integer = odd integer. Always.

The product of an odd and even number will always have 2 as a factor. Therefore, it will always be even.

9

33 The 17th odd positive integer is

The sum of an odd and an even number is odd. Any odd number can be expressed as 2n + 1 (for some integer "n"). Any even number can be expressed as 2m (for another integer, "m"). The sum of the two is 2(m+n) + 1. Since the expression in parentheses is an integer, multiplying it by 2 gives you an even number. Adding 1 makes the entire expression odd.

even integer.

The next odd integer after 40 is 41

The number 71 is an integer, an odd integer, a positive odd integer, and also a prime number.

Only integers are even or odd. We do not call fractions, irrational numbers, imaginary numbers, and so on either even or odd. If a decimal is equal to an integer (for example 24.0 is equal to 24), then it is even if the integer is even or odd if the integer is odd. If a decimal is not equal to an integer (for example 24.1 is not an integer), then it is neither even nor odd.

It is quite easy to prove this using algebra. Suppose x is the smaller of the two odd integer. The fact that x is odd means that it is of the form 2m + 1 where m is an integer. [m integer => 2m is an even integer => 2m + 1 is odd] The next odd integer will be x + 2, which is (2m + 1) + 2 = 2m + 3 The sum of these two consecutive odd integers is, therefore, 2m + 1 + 2m + 3 = 4m + 4 = 4(m + 1) Since m is an integer, m+1 is an integer and so 4(m + 1) represents a factorisation of the answer which implies that 4 is a factor of the sum. In other words, the sum is a multiple of 4.

Yes.