Advertisements
Advertisements
Question
Write whether every positive integer can be of the form 4q + 2, where q is an integer. Justify your answer.
Solution
No, every positive integer cannot be of the form 4q + 2, where q is an integer.
Justification:
All the numbers of the form 4q + 2
Where ‘q’ is an integer, are even numbers which are not divisible by ‘4’.
For example,
When q = 1
4q + 2 = 4(1) + 2 = 6
When q = 2
4q + 2 = 4(2) + 2 = 10
When q = 0
4q + 2 = 4(0) + 2 = 2 and so on.
So, any number which is of the form 4q + 2 will give only even numbers which are not multiples of 4.
Hence, every positive integer cannot be written in the form 4q + 2
APPEARS IN
RELATED QUESTIONS
Define HOE of two positive integers and find the HCF of the following pair of numbers:
105 and 120
Find the largest number which divides 438 and 606 leaving remainder 6 in each case.
Find the largest number which divides 320 and 457 leaving remainders 5 and 7 respectively.
Without actual division, show that each of the following rational numbers is a terminating decimal. Express each in decimal form.
(i) `24/125`
Without actual division, show that each of the following rational numbers is a terminating decimal. Express each in decimal form.
(i) `151/600`
Express each of the following as a rational number in its simplest form:
(i) `0. bar (12)`
Express each of the following integers as a product of its prime factors:
7325
The largest number that will divide 398,436 and 542 leaving remainders 7,11 and 15 respectively is ______.
Show that the square of any positive integer cannot be of the form 6m + 2 or 6m + 5 for any integer m.
For any positive integer n, prove that n3 – n is divisible by 6.
