Question

What is the remainder when 3^40 is divided by 80?
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Answer 1

Answer:

1

Step-by-step explanation:

《 1 》

3^40

=(3^4)^10

≡(80+1)^10

≡1^10(mod 80)

≡ 1 mod80

Answer 2

Answer:

Step-by-step explanation:

Concept:

The quantity that is "left over" after conducting a calculation is referred to as the remnant in mathematics. The residual is the integer that remains after dividing one integer by another to create an integer quotient in mathematics (integer division). The polynomial that remains after dividing one polynomial by another is known as the "remainder" in algebra of polynomials. When a dividend and a divisor are provided, the modulo operation is the one that results in such a remainder.

A residual is also what is left over when two numbers are subtracted from one another, however this is more properly referred to as the difference. Some primary textbooks use this phrase; in everyday speech, "the rest," as in "Give me two dollars back and keep the rest," is used in its place.  Nevertheless, the word "remainder" is still a function is approximated by a series expansion, the phrase "remainder term" is nevertheless used in this context to refer to the incorrect expression ("the rest").

Given:

The number $3^4^ 0$ is divided by $80$.

Find:

We have to find the remainder.

Solution:

Given that the number $3^4^{ 0$ is divided by $80$.

We are aware that each individual product's remnant is a separate product.

We are also aware of $3^4^ 0=81$

Remainder$=3^4^0/80$

                  $=81/80$

                  $=1(mod80)$

Remainder =$1$

Hence the number $3^4^0$ is divided by $80$ we obtain the remainder is $1.$

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