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Question:

Four positive integers p,q,r,s satisfy the following equations:

\begin{align*} pq+2p+q&=348 \\ qr+4q+3r&=373 \\ rs+8r+6s&=544 \end{align*}

What are p,q,r, and s?

p=1; q=1;r=1;s=1;p=1;m=0;n=p+q+r+s;if(n==348 and 373 and 544, goto8, goto next);m=(a*b+b*c+c*d);max(m)==p;print max(m);next:a++;if(a<55, goto5, 0);a=1;b++;if(b<55, goto5, 0);a=1;b=1;c++;if(c<55, goto5,0);a=1;b=1;c=1;d++;if(d<55, goto5, discard=0;

OUTPUT: r = 31 and s = 8 and p = 34 and q = 8

Mar 25, 2020

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I'm sorry about that. I can program a computer to search for the answer, which is what I did. I'm not a mathematician, so I cannot give a mathematical solution. One of the mathematicians here may be able to solve it. Melody, CPhill, EP, Alan, heureka....etc. may take a look at it and see if they can solve it. Good luck.

Mar 26, 2020
edited by Guest  Mar 26, 2020
#2
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heureka: Can you please take a look at this question and see if you can solve it ? Thanks very much.

Mar 27, 2020