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Divisibility (Posted on 2004-01-06) Difficulty: 3 of 5
For how many natural numbers x, is the expression: (x + 2x + 3) divisible by 35 ?

See The Solution Submitted by Ravi Raja    
Rating: 2.5000 (6 votes)

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Solution | Comment 1 of 11
For any natural number x, (x^2+2x+3) mod 5 is congruent to 2, 3 or 4. This means the value of x^2+2x+3 can never be a multiple of 5. Then the answer to the problem is there are no natural numbers x which make x^2+2x+3 a multiple of 35.
  Posted by Brian Smith on 2004-01-06 10:56:19
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