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CBSE Class 10 Answered

Q. 2. Use Euclid division lemma to show that any positive odd integer is of form 6q + 1, or 6q + 3 or 6q + 5, where q is some integers.
Asked by m.sreenu2005 | 24 Jun, 2020, 06:50: AM
answered-by-expert Expert Answer
For any two numbers a and b, there exists q and r such that
a = bq + r  .... Using euclid division algorithm
Here 0 <= r < b
Taking b = 6, a = 6q + r
where 0 <= r < 6
This means r can take the values 0, 1, 2, 3, 4 and 5
When r = 0, 2, 4 the value of a will be 6q, 6q+2, 6q+r which are even
When r = 1, 3, 5
a = 6q + 1, a = 6q + 3, a = 6q + 5 are all odd numbers.
Hence, any positive odd integer is of the form 6q + 1, 6q + 3 or 6q + 5
Answered by Renu Varma | 24 Jun, 2020, 11:37: AM
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