5

Part of 1994 Moldova Team Selection Test

Problems(1)

Find the greatest value of $a^{m_1}+a^{m_2}+\ldots+a^{m_p}$

Source: Moldova TST 1994

m

be a positive integer and

a

a positive real number. Find the greatest value of

a^{m_1}+a^{m_2}+\ldots+a^{m_p}

m_1+m_2+\ldots+m_p=m, m_i\in\mathbb{N},i=1,2,\ldots,p;

1\leq p\leq m, p\in\mathbb{N}