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Topic: Finding Integer Solutions
Replies: 1   Last Post: Jun 14, 1996 7:46 AM

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Richard Pinch

Posts: 27
Registered: 12/6/04
Re: Finding Integer Solutions
Posted: Jun 14, 1996 7:46 AM
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In article <4ppkie$rie@news02.deltanet.com>,
fuji@deltanet.com (Kenneth N. Fujimoto) writes:
|> Are there integer solutions for :
|>
|> 30x^2 + 100x + 27784 = y^2

No. Write this as z^2 - 30y^2 = -831020 = 2^2.5.37.1123
where z = 30x + 50. Since the equation u^2 congruent 30
mod 1123 has no solution, both z and u would have to be
divisible by 1123^2 and so the RHS would be also: contradiction.

Richard Pinch; Queens' College, Cambridge







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