(A) Multiple choice type questions:
1. The product of three consecutive integers is divisible by:
(e)7 (d) none of these
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hii friend your answer is given below...
and the option is (d) none of these
n(n + 1)(n +2)=3m for some integer m and 2 divides 3m. As (2, 3) = 1, Theorem 1.10 tells us 2 | m, say m = 2l for some integer l, then n(n + 1)(n + 2) = 3(2l)=6l. This shows the product is divisible by 6. As the product of three consecutive integers is divisible by 3, so is the product of four consecutive integers.
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Step-by-step explanation:
none of these is the answer
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