Show that any positive odd integer is 4q+1
WebOct 10, 2024 · Here, 1 , 3 are positive odd integers. So, possible values of r is 1 ,3. When r = 1, a = 4 q + 1. It is positive odd integer. When r = 3, a = 4 q + 3. It is positive odd integer. … WebLet a be any odd positive integer and b = 6. Let q be a quotient and r be remainder. Therefore, applying division lemma, we have Chapter Chosen. Real Numbers ... Show that any positive odd integer is of the form 6q + 1, or 6q + 3, or 6q + 5, where q is some integer.
Show that any positive odd integer is 4q+1
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WebSo, for any positive integer q, (4q + 1) and (4q + 3) are odd integers. This is a square which is of the form 4m + 1, where m = (4q2+2q) is an integer. and a2 =(4q+3)2 =16q2+9+24q =4(4q2+6q+2)+1 is a square. Which is of the form 4m + 1, where m = (4q2+6+2) is an integer. Hence, for some integer m, the square of any odd integer is of the form 4m ... WebMar 22, 2024 · Example 3 Show that any positive odd integer is of the form 4q+ 1 or 4q+ 3, where q is some integer. As per Euclid’s Division Lemma If a and b are 2 positive integers, …
WebJan 25, 2024 · Real Numbers: The number system, often known as the numeral system, is a method of expressing numbers. There are two categories of the number system, i.e., real and imaginary numbers. Real numbers are the sum of rational and irrational numbers. All arithmetic operations may be done on these numbers in general. WebMar 18, 2024 · So this implies that $ 4q + 1 $ is always an odd integer. Suppose if $ r = 3 $ , then the equation will become, $ a = 4q + r $ $ a = 4q + 3 $ Since, we know that $ 4q $ is always an even number if we add three to that even number then the number becomes odd. So this implies that $ 4q + 1 $ is always an odd integer. Therefore, any odd integer is ...
WebApr 9, 2024 · From a solid cylinder whose height is 2.4 cm and diameter 1.4 cm, a conical cavity of the same height and same diameter is hollowed out. Find the total surface area …
WebMar 18, 2024 · $ a = 4q + r $ $ a = 4q + 1 $ Since, we know that $ 4q $ is always an even number if we add one to that even number then the number becomes odd. So this implies …
WebMar 16, 2024 · let us start with taking s where a is positive odd integers we apply the division algorithm with a and b = 4 since 0 <_ r < the possible remainder are 0 ,1,2 and 3 this can be 4q or 4q +1 or 4q +2 or 4q +3 where q is the quotient how ever , since odd a cannot be 4q or 4q + 2 any odd integers is form of 4q + 1 or 4 q + 3 Advertisement christine harveyWebNov 25, 2024 · Hence, The square of any odd integer is of the form 4q + 1, for some integer q. ... Show that any positive odd integer is of the form 4q + 1 or 4q + 3, where q is some integer. asked Sep 26, 2024 in Number System by Chandan01 (51.4k points) real numbers; class-10; 0 votes. 1 answer. christine hartunian sinay photosWebLet a be any positive integer by EDL a = bq +r 0 ≤ r < b possible remainders are 0, 1, 2 , 3 this shows that a can be in the form of 4q, 4q+1, 4q+2, 4q+3 q is quotient as a is odd a can't be the form of 4q or 4q+2 as they are even so a ill be in the form of 4q + 1 or 4q+3 hence proved germain ford body shop powellWebProving that the square of any odd integer is of the form 4 q + 1, for some integer q. Apply Euclid's division algorithm, a = b m + r where a , b , m , r are non-negative integers and 0 ≤ r < b . christine harvey bloombergWebAny odd positive integer n can be written as 4q + 1 or 4q + 3. = 8q (2q + 1), is divisible by 8. = 8 (2q 2 + 3q + 1), is divisible by 8. So, from the above equations, it is clear that, if n is an odd positive integer. Try This: If n is an odd integer, then show that n 2 - 1 is divisible by 6. christine harvey church strettonWebJan 30, 2024 · Show that any positive odd integer is of the form 4q+1 or 4q+3, where q is some integer. 18K views 1 year ago 2:39 Show that every positive odd integer is of the form 4q+1 or... christine harvey facebookWebAnswers (1) a=bq+r where b is divisor q is quotient and r is the remainder and . Since divisor is 4, the possible remainder for the condition are 0,1,2,3. Since a is odd, a cannot be 4q and 4q+2 because both are divisible by 2. So the final values of a are 4q+1 and 4q+3. Hence all positive odd numbers are of the form 4q+1 and 4q+3. germain ford sawmill road hours