Question

what is the reminder when a perfect square other than 1 is divided by 3 or 4? give an example each and explain?​

Answer 1

Step-by-step explanation:

—For 3 Remainders can be below = 0,1 or 2

Considering that Square of these remainders are → (0,12,22)=1,4

Rem→0/3=0 & Rem→1/3 = 1 while Rem→4/3 = 1

By this we can say that it’ll always be 0 or 1 for divisor 3

now,

—for 4 Remainders can be below = 0,1,2 or 3

Square of these Remainders = 0, 12,22,32 = 1,4,9

Rem→0/4=0, Rem→(1/4)=1 & Rem→4/4=0 while for Rem→9/4=1

Considering this we can say that only two remainders are possible for divisor 4 = 1 or 0

for Example :—

Series for divisor 3 = 1,1+3,1+3*2,…………………..,1+3n

or Series for divisor 3 = 0,0+3,3*2,………………………,3l

Series for divisor 4 (I case)→ = 0,0+4,4*2,………………,4k

(II case)→1,1+4,1+4*2,………………………………………,1+4m

But in case if we have to consider both divisors for single remainder

then it is always 0 or 1.

Answer 2

Answer:

For 3 Remainders can be below = 0,1 or 2

Considering that Square of these remainders are → (0,12,22)=1,4  

Rem→0/3=0 & Rem→1/3 = 1 while Rem→4/3 = 1

By this we can say that it’ll always be 0 or 1 for divisor 3

now,

—for 4 Remainders can be below = 0,1,2 or 3

Square of these Remainders = 0, 12,22,32   =  1,4,9

Rem→0/4=0, Rem→(1/4)=1 & Rem→4/4=0 while for Rem→9/4=1