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| 1. |
M =3m + 1 |
| Answer» Let n be an arbitrary positive integer.On dividing n by 3, let m be the quotient and r be the remainder.The positive integer is in the form of 3m or (3m + 1) or (3m + 2)Then, by Euclid\'s division lemma, we haven = 3m + r, where {tex}0 \\leq r < 3{/tex}.{tex}\\therefore{/tex}\xa0n = 3m or (3m +1) or (3m + 2), for some integer m.Thus, any positive integer is of the form 3m or (3m + 1) or (3m + 2) for some integer m. | |