Question 1185809
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I am guessing that the other tutor misinterpreted the problem because of the awkward way it was stated.<br>
Your statement:<br><pre>
What is the fourth positive integer N such that the product of any two increased by 1 of the numbers 3,8,21,N is a square</pre>
I believe, for clarification, that the intended statement of the problems should be this:<br><pre>
What is the fourth positive integer N such that the product of any two of the numbers 3,8,21,N, increased by 1, is a square</pre>
If that is the intended meaning of the problem, then the given conditions are satisfied:
3*8+1=25 = 5^2
3*21+1=64 = 8^2
8*21+1=169 = 13^2
If that is what the problem was intended to say, then re-post....<br>
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I note that the numbers involved in the problem are 3, 5, 8, 13, and 21, which are successive numbers in the Fibonacci sequence; so I suspect the answer might be found in the Fibonacci sequence.  But I haven't found it.<br>
55 ALMOST works:
21*55+1=1156=34^2
8*55+1=441 = 21^2
but 3*55+1=166 is not a perfect square....<br>