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Introduction to Numbers

If a, b and c...

Question

If a, b and c are positive integers and (a - b)c = 0, which statement must be true?

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Solution

Either a=b or c=0 but c can't be equal to zero, as it is a positive integer.

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Similar questions

Q. Which of the following statements are true?
(i) The product of a positive and a negative integer is negative.
(ii) The product of three negative integers is a negative integer.
(iii) Of the two integers, if one is negative, then their product must be positive.
(iv) For all non-zero integers a and b, a × b is always greater than either a or b.
(v) The product of a negative and a positive integer may be zero.
(vi) There does not exist an integer b such that for a> 1, a × b = b × a = b.

Q. Euclid's division lemma sates that for any positive integers a and b, there exist unique integers q and r such that a = bq + r, where r must satisfy

(a) 1 < r < b
(b) 0 < r ≤ b
(c) 0 ≤ r < b
(d) 0 < r < b

If a, b and c are positive integers and (a - b)c = 0, which statement must be true?

Q. Which of the following statements must be true whenever

n, a, b

c

are positive integers such that

n < a, c > a

b > c

?

Q. Euclid's division lemma states that for two positive integers a and b, there exists unique integers q and rr such that

a = b q + r

, where r must satisfy

0 \leq r \leq b

is this statement true?

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