2

Part of 2003 IMC

Problems(2)

51 elements of a field

Source: IMC 2003 day 1 problem 2

a_1, a_2,...,a_{51}

be non-zero elements of a field of characteristic

p

. We simultaneously replace each element with the sum of the 50 remaining ones. In this way we get a sequence

b_1, ... , b_{51}

. If this new sequence is a permutation of the original one, find all possible values of

p

superior algebrasuperior algebra unsolved

Limit of an integral

Source: IMC 2003 day 2 problem 2

\lim_{x\rightarrow 0^+}\int^{2x}_x\frac{\sin^m(t)}{t^n}dt

m,n\in\mathbb{N}

calculusintegrationlimittrigonometrylogarithmsinequalitiesreal analysis