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Class 10
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show that any positive odd integer is of the form...

Question:
Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer.

Answer:

Let a be any positive integer b = 6. Then by Euclid’s algorithm,
a = 6q + r for some integer q ≥ 0

So, values of r we get, r = 0, 1, 2, 3, 4, 5

When, r = 0, then, a = 6q + 0,

similarly for r = 1, 2, 3, 4, 5 the value of a is 6q+1, 6q+2, 6q+3, 6q+4 and 6q+5 respectively.

If a = 6q, 6q+2, 6q+4, then a is even and divisible by 2.

Therefore, any positive odd integer is in the form of 6q+1, 6q+3, 6q+5

Where q is some integer.

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Question:
Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer.

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Question: Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer.

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Question:
Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer.