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Positive integers a and b are such that `a+b=a/b+b/a` What is the value of `a^2 +b^2`?

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RESONANCE ENGLISH-NUMBER THEORY-Exercise -2 (PART - I)
  1. How many non-negative integral values of x satisfy the equation [x/5]=...

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  2. What is the sum of the squares of the roots of the equation x^(2)-7[x]...

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  3. Let S(M) denote the sum of the digits of a positive integer M written ...

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  4. To each element of the set S = {1, 2, 3.....1000}, a colour is assigne...

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  5. What is the smallest positive integer k such that k(3^(3) + 4^(3)+ 5^(...

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  6. One morning, each member of manjul's family drank an 8-ounce mixture o...

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  7. For how many natural numbers n between 1 and 2014 (both inclusive) is ...

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  8. What is the greatest possible perimeter of a right angled triangle wit...

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  9. Positive integers a and b are such that a+b=a/b+b/a What is the value...

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  10. Let n be the largest integer that is the product of exactly 3 distinct...

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  11. The digits of a positive integer n are four consecutive integers in de...

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  12. Find the total number of solutions to the equation x^2 + y^2 = 2015 wh...

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  13. a, b, c, d are integers such that ad + bc divides each of a, b, c and ...

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  14. Suppose an integer, a natural number n and a prime number p satisfy th...

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  15. Let p, q be prime numbers such that non n^(3pq)-n is a multiple of 3p...

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  16. For each positive integer n, consider the highest common factor hn of ...

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  17. If a,b,c ge 4 are integers, not all equal, and 4abc = (a + 3) (b + 3)...

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  18. Let a and b natural numbers such that 2a - b, a - 2b and a + b are all...

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  19. Let N = 6 + 66 + 666 + ... + 666....66, where there are hundred 6's in...

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  20. Determine the sum of all possible positive integers n, the product of ...

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