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For positive real numbers x and y, define their special mean to be average of their arithmetic and geometric means. Find the total numbe of pairs of integers `(x,y)` with `x le y,` from the set of numbers `(1,2,……,2016),` such that the special mean of x and y is a perfect square.

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506
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RESONANCE-SEQUENCE & SERIES -EXERCISE -2 (PART -I PREVIOUS ASKED QUESTION FOR PRE RMO)
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  8. Consider the sequence 1,3,3,5,5,5,5,5,7,7,7,7,7,7,7,…… and evaluate it...

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  10. Let S=1 + (1)/(sqrt2) + (1)/(sqrt3) + (1)/(sqrt99) + (1)/(sqrt100). Fi...

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  12. Let u,v,w be real numbers in geometric progression such that u gt v gt...

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  13. Let the sum sum ( n =1) ^(g) (1)/(n ( n +1) ( n +2)) written in its lo...

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  14. Suppose x is a positive real number such that {x}, [x] and x are in th...

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  15. Five distinct 2-digit numbes are in a geometric progression. Find the ...

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  16. Let N = 6 + 66+ 666+…+ 666…66, where there are hundred 6's in the last...

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  17. What is the value of sum (1+j = odd 1 le | lt | le 10) (i +j) - sum(1 ...

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