My Math Forum  

Go Back   My Math Forum > High School Math Forum > Elementary Math

Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion

LinkBack Thread Tools Display Modes
January 3rd, 2014, 06:42 AM   #1
Joined: Aug 2012

Posts: 40
Thanks: 3

Integer Solutions to Z-sZ+p=0

Hey there, guys!
Let the equation Z-sZ+p=0 with integer coefficients. Then, the equation has integer solutions if, and only if, s-4p is a perfect square.
But is there an "easier" or "shorter" way to determine when the equation has or hasn't solutions?
For example, consider the equation:

z-3187z+2539212 = 0
It has two solutions: 1588, 1599

But it may be a little boring to calculate s-4p and later checking if it's a perfect square if both numbers are too high. So, is there an easier way?

So far, I only could derive the trivial:
if both s and p are odd, then there's no solution;
if p is prime, then there's a solution iff s = p+1;
if the equation is on the form z-2kz+k=0 then z=k;

But those are too specific and not very helpfull at all... Also, in the last case checking that p = k and s = 2k doesn't help for large integers...
AlephUser is offline  

  My Math Forum > High School Math Forum > Elementary Math

integer, solutions, zsz

Thread Tools
Display Modes

Similar Threads
Thread Thread Starter Forum Replies Last Post
Finding the number of Integer Solutions devenj Number Theory 1 November 30th, 2012 05:29 AM
Integer solutions proglote Number Theory 4 June 8th, 2011 02:41 PM
Some equations having integer solutions proglote Number Theory 4 April 19th, 2011 10:06 AM
all integer solutions of 3^m-2^n=+-1 calligraphy Number Theory 7 April 13th, 2011 01:56 PM
x^5+31=y^2 has no integer solutions elim Number Theory 4 April 5th, 2010 02:05 PM

Copyright © 2017 My Math Forum. All rights reserved.