Difference between revisions of "PUMAC 2008-2009 Number Theory A problems"

Revision as of 22:19, 4 February 2009

1. (2 points) How many zeros are there at the end of 792! when written in base 10?

2. (3 points) Find all integral solutions to $x^y-y^x=1$ .

3. Find the largest integer $n$ , where $2009^n$ divides $2008^2009^(2010)+2010^2009^(2008)$ .

Revision as of 22:18, 4 February 2009 (view source) Lss1609 (talk \| contribs) (New page: 1. (2 points) How many zeros are there at the end of 792! when written in base 10? 2. (3 points) Find all integral solutions to <math>x^y-y^x=1</math>. 3. Find the largest integer <math>...)		Revision as of 22:19, 4 February 2009 (view source) Lss1609 (talk \| contribs) Newer edit →
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	2. (3 points) Find all integral solutions to <math>x^y-y^x=1</math>.		2. (3 points) Find all integral solutions to <math>x^y-y^x=1</math>.

−	3. Find the largest integer <math>n</math>, where <math>2009^n</math> divides <math>2008^(2009^(2010))+2010^(2009^(2008))</math>.	+	3. Find the largest integer <math>n</math>, where <math>2009^n</math> divides <math>2008^2009^(2010)+2010^2009^(2008)</math>.