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Primed to Square (Posted on 2013-02-15) Difficulty: 3 of 5
What is the largest prime p that makes sqrt(17p+625) an integer?

No Solution Yet Submitted by Danish Ahmed Khan    
Rating: 4.0000 (2 votes)

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Solution p Comment 3 of 3 |
sqrt(17p+625)=x
17p+625=x^2
17p=x^2-625
17p=(x+25)(x-25)

Therefore, x+25 and x-25 are either 1 and 17p, or 17 and p.

Case 1:x+25=1, x-25=17p
x=-24, but x-25=-49 is not divisible by 17.

Case 2:x+25=17p, x-25=1
x=26 and x+25=51, so p=3.

Case 3:x+25=17, x-25=p
x=-8, but x-25=-33 is not prime.

Case 4:x+25=p, x-25=17
x=42, so p=67.

Therefore, the answers are 3 and 67.


  Posted by Math Man on 2013-02-15 21:54:56
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