Terminating Decimals in Set Notation Problem

Number Theory Level pending

If the set of terminating decimals can be represented by { a x b × y c ∣ { a , b , c } ∈ Z a n d { x , y } ∈ P } \left\{\frac{a}{x^b \times y^c}\mid\{a,b,c\}\in\mathbb{Z}\ \mathrm{and}\ \{x,y\}\in\mathbb{P}\right\} , where x and y are constants, then find ( x + y ) 2 (x+y)^{2} .


The answer is 49.

Mr.Person 12345 by Mr.Person 12345 , 21, USA

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1 solution

Mr.Person 12345
Oct 27, 2017

Any terminating decimal can be written as ABCDE.../10000...

= ABCDE.../ 1 0 n 10^{n}

= ABCDE.../( 2 n × 5 n 2^{n}\times 5^{n} )

so x and y are 2 and 5.

( 2 + 5 ) 2 = 49 (2+5)^{2}=49

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