Can we find integers x and y such that f,g,h are strictely positive integersLet a &gt; 2 and b &gt; 2 two strictely positive integers. Let us consider the following quantities: f = x y + a y + a 2 b y g = a ( y + a ) x y + a y + a 2 b y 2 x h = y + a b My question is:Can we find integers x and y (not necessarly positive) such that f,g,h are strictely positive integers. Or at lest how one can proves that they are exist.

Question

Can we find integers x and y such that f,g,h are strictely positive integersLet   a  &amp;gt;  2 and   b  &amp;gt;  2 two strictely positive integers. Let us consider the following quantities:  f  =                    x        y        +        a        y        +                  a                      2                                      b        y              g  =  a  (  y  +  a  )                    x        y        +        a        y        +                  a                      2                                      b                  y                      2                          x              h  =                    y        +        a            b      My question is:Can we find integers x and y (not necessarly positive) such that f,g,h are strictely positive integers. Or at lest how one can proves that they are exist.

rcampas4i · Accepted Answer

If we let,  a  =  (  b  k  −  1  )  y  ,    x  =  b  ythen the three polynomials lose their denominators,  (  b      k    2    −  k  +  1  )  y  ,    (  b  k  −  1  )  (  b      k    2    −  k  +  1  )  k  y  ,    k  yand are positive integers if   b  ,  k  ,  y are positive integers.

Can we find integers x and y such that f,g,h are strictely positive integers Let a>2 and b>2 two strictely positive integers. Let us consider the following quantities: f= (xy+ay+a^(2))/(by) g=a(y+a)(xy+ay+a^(2))/(by^(2)x) h=(y+a)/(b)

Answered question

Answer & Explanation

New Questions in Pre-Algebra