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Algebra Level 2

3^19 = 11a2261467


The answer is 6.

Sunil Pradhan by Sunil Pradhan , 68, India

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5 solutions

Sunil Pradhan
Jan 2, 2015

3^19 = 3^2 × 3^17 as 3^2 i.e. 9 is a factor of 3^19 applying test of divisibility

sum of digits 1+1+a+2+2+6+1+4+6+7=30+a divisible by 9 then a = 6

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Chinmay Agarwal
Feb 15, 2015

3^19=3^2x3^17 therefore it is divisible by 9(3^2) => 11a2261467 should be divisible by 9 => digits should add up to give a multiple of 9 by that we have a=6

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Vishal S
Jan 2, 2015

Sum of the digits of 3^19 is 1+1+a+2+2+6+1+4+6+7=30+a

since 9 is a factor of 3^19

therefore the sum of the digits must be divisible by 9

If 30+a should be divisible by 9, 30+a must be 36 => a=6

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Ivan dennys Opit
Jan 2, 2015

9 is factor of 3^19 so the sum digits of 3^19 can divide by 9. 1+1+a+2+2+6+1+4+6+7=30+a, so a is 6

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Nelson Mandela
Jan 2, 2015

3^19 is 1162261467.

so "a" must be 6.

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Explaination?

3 19 = 11 a 2261467 3^{19} = 11a2261467

So the sum of the digits should be divisible by 9 , thus a = 6

U Z - 6 years, 5 months ago

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Thanks for the clear solution!

Nelson Mandela - 6 years, 5 months ago

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