How will you prove that any positive odd integer is of the form 6q 1 or 6q 3 or 6q 5 where Q is some integer?

Clearly, 6q + 1, 6q + 3 and 6q + 5 are of the form 2k + 1, where k is an integer. Therefore, 6q + 1, 6q + 3 and 6q + 5 are not exactly divisible by 2. Hence, these expressions of numbers are odd numbers and therefore any odd integers can be expressed in the form 6q + 1 or 6q + 3 or 6q + 5.

In which form every positive odd integer can be written when p is some integer?

2q+1
We know that, odd integers are 1,3,5…. So, it can be written in the form of 2q+1.

What is positive odd integer?

An odd number is an integer when divided by two, either leaves a remainder or the result is a fraction. One is the first odd positive number but it does not leave a remainder 1. Some examples of odd numbers are 1, 3, 5, 7, 9, and 11. An integer that is not an odd number is an even number.

Can any positive odd integer is of the form 8 Q 6?

No, any positive odd integer cannot be of the form 8q+6 as if we simplify it we can write it as multiple of 2 as: 2(4q+3). Now, any integer which a multiple of two is an even number not an odd number.

How will you prove that any positive odd integer is in the form of?

Show that any positive odd integer is of the form 6q + 1 or 6q + 3 or 6q + 5; where q is some integer. Answer: According to Euclid’s Division Lemma if we have two positive integers a and b, then there exist unique integers q and r which satisfies the condition a = bq + r where 0 ≤ r < b.

Is some an integer?

An integer (pronounced IN-tuh-jer) is a whole number (not a fractional number) that can be positive, negative, or zero. Examples of integers are: -5, 1, 5, 8, 97, and 3,043. Examples of numbers that are not integers are: -1.43, 1 3/4, 3.14, . 09, and 5,643.1.

When q is some integer in which form can every positive even integer can be written?

Answer: Show that every positive even integer is of the form 2q and every positive odd integer is of the form 2q + 1, where q is some integer.

How do you find odd positive integers?

To identify an odd number we can directly divide it by 2. If the number is exactly divisible by 2 it is not an odd number. For example, 4 is not an odd number as it is exactly divisible by 2.

Can any positive odd integer be of the form 8q 1?

So r can be 0, 1, 2, 3, 4, 5, 6 or 7. We need only odd numbers. Since 8q, 8q+2, 8q+4, and 8q+6 are divisible by 2, they are even numbers. So any odd integer can be written as any one of ch are (8q+1, 8q+3, 8q+5 or 8q+7.)

What is Euclid’s Division Lemma?

Euclid’s division lemma states that for any two positive integers, say ‘a’ and ‘b’, the condition ‘a = bq +r’, where 0 ≤ r < b always holds true. Mathematically, we can express this as ‘Dividend = (Divisor × Quotient) + Remainder’. Euclid, a Greek mathematician, devised Euclid’s division lemma.

Is 1 a integer number?

The integers are …, -4, -3, -2, -1, 0, 1, 2, 3, 4, — all the whole numbers and their opposites (the positive whole numbers, the negative whole numbers, and zero). Fractions and decimals are not integers.