# Question about problem 53 in Problem Solving and Selected Topics in Number Theory

I solved problem 53 in Problem-solving and selected topics in Number Theory. The problem was: Find the sum of all positive integers that are less than 10,000 and whose square divided by 17 leaves remainder 9. I added my solution and the solution in the book as images. I think that my solution is right. Please confirm or explain.

• I get the same answer as you; there is probably a flaw in the book's proof but it seems the beginning is missing. – fkraiem Nov 26 '14 at 15:13
• I included only the last page of 3. – nilo de roock Nov 26 '14 at 17:18

Note that $$\overline{x}_i=17i-3$$ is a solution for $i=1,\cdots, 588.$ But, $$x_i=17i+3$$ is a solution for $i=0,\cdots, 588.$ Thus, $x_0=3$ is a solution that is not computed in the book. That is, your answer is correct.