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 2aba2+b2, kapjuk, hogy n4=(a+b)22(a2+b2)=2n3, ahonnan n2. 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 solutionss.
Problems in Mathematics of KöMaL, April 2007