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Find the number of positive integers x f...

Find the number of positive integers x for which `f(X)=x^(3)-8x^(2)+20x-13,` is a prime number.

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RESONANCE-NUMBER THEORY-Exercise -1 (PART - I)
  1. Does there exist an integer such that its cube is equal to 3n^(2) + 3n...

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  2. Let A be the sum of the digits of the number (4444)^(4444) and B be t...

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  3. For how many integers n is sqrt(9-(n+2)^2) a real number?

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  4. The number of prime numbers less than 1 million whose digital sum is 2...

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  5. An eight digit number is a multiple of 73 and 137. If the second digit...

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  6. The number of natural numbers n for which (15n^2+8n+6)/n is a natural...

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  7. Let A be the least number such that 10A is a perfect square and 35 A i...

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  8. The number of 2 digit numbers having exactly 6 factors is :

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  9. The number of positive integers 'n' for which 3n-4, 4n-5 and 5n - 3 a...

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  10. Find the number of positive integers x for which f(X)=x^(3)-8x^(2)+20x...

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  11. a, b, c are digits of a 3-digit number such that 64a + 8b + c = 403, t...

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  12. N is a five digit number. 1 is written after the 5 digit of N to make ...

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  13. The sum of all values of integers n for which (n^2-9)/(n-1) is also an...

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  14. The number of natural number pairs (x, y) in which x gt y and 5/x+6/y...

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  15. The number of positive integer pairs (a, b) such that ab - 24 = 2b is

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  16. A = (2+ 1) (22 + 1) (2 + 1)..... (2^(2048) + 1) The value of (A + 1)^(...

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  17. The least positive integer n such that 2015^(n) + 2016^(n) + 2017^(n) ...

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  18. The number of pairs of relatively prime positive integers (a, b) such ...

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  19. The four digit number 8ab9 is a perfect square. The value of a^(2) + b...

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  20. a, b are positive real numbers such that 1/a+9/b=1 The smallest value ...

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