
Elementary Math Fractions, Percentages, Word Problems, Equations, Inequations, Factorization, Expansion 
 LinkBack  Thread Tools  Display Modes 
January 3rd, 2014, 05:42 AM  #1 
Member Joined: Aug 2012 Posts: 40 Thanks: 3  Integer Solutions to Z²sZ+p=0
Hey there, guys! Let the equation Z²sZ+p=0 with integer coefficients. Then, the equation has integer solutions if, and only if, s²4p 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: z²3187z+2539212 = 0 It has two solutions: 1588, 1599 But it may be a little boring to calculate s²4p 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 z²2kz+k²=0 then z=k; But those are too specific and not very helpfull at all... Also, in the last case checking that p = k² and s = 2k doesn't help for large integers... 

Tags 
integer, solutions, z²sz 
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 04:29 AM 
Integer solutions  proglote  Number Theory  4  June 8th, 2011 01:41 PM 
Some equations having integer solutions  proglote  Number Theory  4  April 19th, 2011 09:06 AM 
all integer solutions of 3^m2^n=+1  calligraphy  Number Theory  7  April 13th, 2011 12:56 PM 
x^5+31=y^2 has no integer solutions  elim  Number Theory  4  April 5th, 2010 01:05 PM 