Mathematical and Physical Journal
for High Schools
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Problem B. 3994. (April 2007)

B. 3994. Find all non-negative integers n for which there are non-negative numbers a and b, such that n2=a+b és n3=a2+b2.

(3 pont)

Deadline expired on May 15, 2007.


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

Megoldás: Mivel 2ab\lea2+b2, kapjuk, hogy n4=(a+b)2\le2(a2+b2)=2n3, ahonnan n\le2. Ha n=0, akkor a=b=0, ha n=1 akkor a=1, b=0, ha pedig n=2, akkor a=b=2 megfelelő.


Statistics:

133 students sent a solution.
3 points:97 students.
2 points:14 students.
1 point:10 students.
0 point:4 students.
Unfair, not evaluated:8 solutions.

Problems in Mathematics of KöMaL, April 2007