Be careful

Number Theory Level 3

Let $A$ denote the sum of all integers whose square is a 4 digit number;

$B$ denote the sum of all natural numbers below 100;

$C$ denote the sum of all integers less than 1000 which can be expressed as a perfect 100th power.

Evaluate $\frac {A+B}{C} + \frac {A+C}{B}$ .

9472.88 Infinite 9372.89 Interdeterminant 5050 4950

1 solution

Ronak Agarwal
Feb 10, 2015

Too simple $A=0 ,B=4950 , C=1$

Try to post a solution with relevant working instead of one without.

c = 0 because the possible integers are 1 and -1 therefore answer should be infinite.....

Nikhil Moghe - 6 years, 2 months ago

-1 cannot be $n^{100}$ as any number raised to even power is positive. So $c=0 + 1 = 1$

Vishwak Srinivasan - 6 years, 2 months ago

We are not in a need of the 100th power but the integer whose 100th power is less than 1000. so c should be -1+1=0

Aravind Vishnu - 6 years, 1 month ago