Question
Asked Aug 19, 2019
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let M be the greatest integer less than 30 such that M!(M+1)!/2 is a perfect square. Let N be the greatest integer that divides C^4-C^2 for the integers C>1. Find M+N

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Expert Answer

Step 1

Refer to the question we have to find the value of M and N for the given conditions.

For solve the first condition wich is given for expressio should be perfect square  and the expression is as,

 

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M!(M+M 30 2

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Step 2

Now for greatest integer value of M<30 the expression M!(M+1)!/2  should be a perfect square.

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M( М+1)! м:(М+1)(М+1-1)! 2 2 As, n!- n-(п-1):(п-1).1! M:(М+1)(М+1—-1)! М+1 (му? 2

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Step 3

Now since (M!)^2 will always be perfect square so The value of M will depend on (M+1)/2 this term should be such that it is perfect square then only whole te...

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M 1 (M!) = perfect square root as M < 30 2

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Math

Algebra