Question

2. Use Euclid division lemma to show that any positive odd integer is of the form 69 + 1 or 69 + 3 or 69 +5, where q is some integers.

Sol. Let 'a' be an odd positive integer. Let us now apply division algorithm with a and b = 6. 05r < 6, the possible remainders are 0, 1, 2, 3, 4 and 5. i.e., 'a' can be 6q or 6q+1 or 60 + 2 or 69 + 3 or 6 + 4 or 60 + 5, where the quotient. q is But 'a' is taken as an odd number, :. a can't be 69 or 69 + 2 or 6q+ 4. :: Any odd integer is of the form 69 + 1,69 + 3 or 60 + 5.

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Answer 1

Answer:

the question was wrong it can be written as 69,69+1,69+4.....