Write whether every positive integer can be o | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(B) No,every positive integer cannot be of the form $4q + 2$.According to Euclid's Division Lemma,for any positive integer $b$ and a positive integer

Vedclass · Accepted Answer

No

Vedclass · Answer

(B) No,every positive integer cannot be of the form $4q + 2$.According to Euclid's Division Lemma,for any positive integer $b$ and a positive integer $a = 4$,there exist unique integers $q$ and $r$ such that $b = 4q + r$,where $0 \le r This means the possible values for the remainder $r$ are $0, 1, 2,$ and $3$.Therefore,any positive integer $b$ can be expressed in one of the following forms: $4q, 4q + 1, 4q + 2,$ or $4q + 3$.Since a positive integer can also take the forms $4q, 4q + 1,$ or $4q + 3$,it is not restricted to only the form $4q + 2$.

Write whether every positive integer can be of the form $4q + 2$,where $q$ is an integer. Justify your answer.

Similar Questions

$\frac{47}{500}$ has $\ldots$ digits after the decimal point in its terminating decimal expansion.

If $n$ is a positive even integer,then $n(n+1)(n+2)$ is divisible by $\ldots \ldots \ldots \ldots .$

Find the largest number that divides $2053$ and $967$ and leaves a remainder of $5$ and $7$ respectively.

Without actually performing the long division,find if $\frac{987}{10500}$ will have a terminating or non-terminating (repeating) decimal expansion. Give reasons for your answer.

According to Euclid's division lemma,for given positive integers $a$ and $7$,there exist unique non-negative integers $q$ and $r$ such that $a = 7q + r$; where..........

Vedclass Test Series

Exam Paper Generator

Online Exam Module