Let C be a positive integer such that C + 7 is divisible by 5. The smallest positive integer n (2) such that C + n 2 is divisible by 5 is

Question

Let C be a positive integer such that C + 7 is divisible by 5. The smallest  positive integer n (>2) such that C + n 2 is divisible by 5 is

ganeshie8 · Answer

C+7 is divisible by 5

=>

C+7 = 5k

C = 5k-7

anonymous · Answer

In the question please note its C +n^2 ie n square....
$$C + n ^{2}$$

ganeshie8 · Answer

$C + n^2   =   5k -7 + n^2$

ganeshie8 · Answer

clearly $5k$ is divisible by 5
so you need to wry oly about $-7+n^2$

ganeshie8 · Answer

next, think wat digits are possible in in units place for a square number : $n^2$

ikram002p · Answer

nice qs ...

ikram002p · Answer

cosider the last digite of n^2
0 1 4 5 6 9 -
7 7 7 7 7 7 
ـــــــــــــــــــــــــــــــــ
7  6 3 2 1 3

ikram002p · Answer

the last one 2

ikram002p · Answer

so i guss n^2-7 never devide 5 right ?

ganeshie8 · Answer

Yes

ganeshie8 · Answer

$n^2 - 7 \equiv   n^2+3 (\mod{5} ) $

ganeshie8 · Answer

and n^2 never gives 2 or 7 as last digit

ikram002p · Answer

aha right :)