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Natural Numbers

15 Prove that...

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15 Prove that every positive integer different from 1 can be expressed as a product of a non-negative power of 2 and an odd number.

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Q. Prove that every positive integer different from

1

can be expressed as a product of a non-negative power of

2

and an odd number.

Q. Is it true that every positive integer different from 1 can be expressed as a product of non-negative power of 2 and an odd number. What is the odd number when there are no prime factors.

Q. Problems Set at an Oral Examination.
Show that every odd number can be represented as a difference of the squares of two integers.

Q. Which of the following statements are true and which are false?

(i) The product of a positive and a negative integer is negative.
(ii) The product of two negative integers is a negative integer.
(iii) The product of three negative integers is a negative integer.
(iv) Every integer when multiplied with −1 gives its multiplicative inverse.
(v) Multiplication on integers is commutative.
(vi) Multiplication on integers is associative.
(vii) Every nonzero integer has a multiplicative inverse as an integer.

Q. Every integer '

a

' is a rational number, as '

a

' can be expressed as

\frac{a}{1}

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