Mathematical and Physical Journal
for High Schools
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Problem K. 269. (November 2010)

K. 269. Explain why there is no pair (x,y) of integers such that xy(x2-y2)=2925?

(6 pont)

Deadline expired on December 10, 2010.


Sorry, the solution is available only in Hungarian. Google translation

Megoldás. \(\displaystyle xy(x^2-y^2)=xy(x+y)(x-y)\) négytényezős szorzat (\(\displaystyle x\), \(\displaystyle y\) egészek) biztos, hogy páros, ugyanis ha \(\displaystyle x\) vagy \(\displaystyle y\) páros, akkor azért, ha mindkettő páratlan, akkor az összegük (és a különbségük is) páros. A szorzat tehát nem lehet 2925, mert az páratlan.


Statistics:

205 students sent a solution.
6 points:127 students.
5 points:17 students.
4 points:9 students.
3 points:7 students.
2 points:8 students.
1 point:5 students.
0 point:24 students.
Unfair, not evaluated:8 solutions.

Problems in Mathematics of KöMaL, November 2010