Advertisements
Advertisements
प्रश्न
If p1 and p2 are two odd prime numbers such that p1 > p2, then
विकल्प
an even number
an odd number
an odd prime number
a prime number
उत्तर
Let the two odd prime numbers `p_1` and `p_2`be 5 and 3.
Then,
`p_1^2=5^2`
=25
and
`p_1^2-p_2^2=25-9`
`=16`
16 is even number.
Take another example, with `p_1` and `p_2`be 11 and 7.
Then,
Take another example, with `p_1` and `p_2`be 11 and 7.
Then,
`p_1^2=11^2`
=121
and
`p_1^2=7^2`
=49
thus,
`p_1^2- p_2^2=121-49`
=72
72 is even number.
Thus, we can say that `p_1^2- p_2^2` is even number
In general the square of odd prime number is odd. Hence the difference of square of two prime numbers is odd
Hence the correct choice is (a).
APPEARS IN
संबंधित प्रश्न
Prove that the square of any positive integer is of the form 5q, 5q + 1, 5q + 4 for some integer q.
Express the HCF of 468 and 222 as 468x + 222y where x, y are integers in two different ways.
What is the largest number that divides 626, 3127 and 15628 and leaves remainders of 1, 2 and 3 respectively.
Three sets of English, Mathematics and Science books containing 336, 240 and 96 books respectively have to be stacked in such a way that all the books are stored subject wise and the height of each stack is the same. How many stacks will be there?
The sum of two prime number is always a prime number (True/ False).
Two numbers have 12 as their HCF and 350 as their LCM (True/False).
In Q.No. 7, HCF (a, b) is
Show that every positive odd integer is of the form (4q + 1) or (4q + 3), where q is some integer.
Euclid’s division lemma states that for positive integers a and b, there exist unique integers q and r such that a = bq + r, where r must satisfy
Write whether the square of any positive integer can be of the form 3m + 2, where m is a natural number. Justify your answer.
