Digital Sum !!

Number Theory Level 2

123 4 , c 123 4 56 7 , c 123 4 56 7 89 10 123{\color{#3D99F6} 4 } , \phantom{c} 123{\color{#3D99F6}4}56{\color{#D61F06}7}, \phantom{c} 123{\color{#3D99F6}4}56{\color{#D61F06}7}89{\color{#20A900}10} Naruto creates some of the above number by concatenation of consecutive numbers, he notices such numbers are not evenly divisible by 3 when unit place number terminates at 4 , 7 ,10, 13 or in the sequence of 3 m + 1 3m +1 where m ∈ N m\in\mathbb N .

Is it true that the number created in that way is not evenly divisible by 3?

Yes Cannot be determined. No

Naren Bhandari by Naren Bhandari , 21, India

This section requires Javascript.
You are seeing this because something didn't load right. We suggest you, (a) try refreshing the page, (b) enabling javascript if it is disabled on your browser and, finally, (c) loading the non-javascript version of this page . We're sorry about the hassle.

1 solution

X X
Jul 21, 2018

Digit sum is ( 1 + 3 m + 1 ) ( 3 m + 1 ) 2 = ( 3 m + 2 ) ( 3 m + 1 ) 2 \dfrac{(1+3m+1)(3m+1)}{2}=\dfrac{(3m+2)(3m+1)}{2} ,which is not a multiple of 3.

1 Helpful 0 Interesting 0 Brilliant 0 Confused

0 pending reports

×

Problem Loading...

Note Loading...

Set Loading...