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Part of 1999 Iran MO (2nd round)

Problems(2)

Powers of 2 - Iran NMO 1999 (Second Round) Problem1

Source:

Does there exist a positive integer that is a power of

2

and we get another power of

2

by swapping its digits? Justify your answer.

modular arithmeticnumber theory proposednumber theory

m= a_1/1+... - Iran NMO 1999 (Second Round) Problem4

Source:

Find all positive integers

m

such that there exist positive integers

a_1,a_2,\ldots,a_{1378}

m=\sum_{k=1}^{1378}{\frac{k}{a_k}}.

inductionnumber theory proposednumber theory