# Difference between revisions of "2021 CIME I Problems/Problem 2"

Dark adonis (talk | contribs) (Created page with "==Problem 2== For digits <math>a, b, c,</math> with <math>a\neq 0,</math> the positive integer <math>N</math> can be written as <math>\underline{a}\underline{a}\underline{b}\u...") |
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Next note that <math>b = 3a</math> since <math>b<5</math> and <math>a>0</math> the only solution is <math>b=3</math>,<math>a=1</math> | Next note that <math>b = 3a</math> since <math>b<5</math> and <math>a>0</math> the only solution is <math>b=3</math>,<math>a=1</math> | ||

Thus in base 10 the number is <math>810+30=840</math> | Thus in base 10 the number is <math>810+30=840</math> | ||

+ | |||

+ | ==Video Solution by Punxsutawney Phil== | ||

+ | https://www.youtube.com/watch?v=VEbEouF2D0g&t=0s |

## Latest revision as of 14:06, 19 January 2021

## Problem 2

For digits with the positive integer can be written as in base and in base . Find the base- representation of .

## Solution

Consider the different representations of the number and equate them:

Note that c can't contribute since it is less than 5 so Next note that since and the only solution is , Thus in base 10 the number is