In this problem, we study the form of the square of a positive integer. We are required to prove that the square of any positive integer can be written in the form 3m or 3m + 1, but never in the form 3m + 2. Question Prove that the square of any positive integer is […]
In this problem, we prove a property of integers expressed in algebraic form. We are required to show that the square of any positive integer of the form 5q + 1 is again of the same form. Question Prove that the square of any positive integer of the form 5q + 1 is of the
Prove that the square of any positive integer of the form 5q + 1 is of the same form Read More »
In this problem, we study the relationship between two algebraic forms of a positive integer. We are required to prove that every integer of the form 6q + 5 can also be written in the form 3q + 2 for some integer q, but the converse statement is not true. Question Prove that if a
In this problem, we prove a basic divisibility property of integers. We are required to show that for every positive integer n, the expression n³ − n is always divisible by 6. Question For any positive integer n, prove that n³ − n is divisible by 6. Solution Consider the expressionn³ − n. Taking n
For any positive integer n, prove that n³ − n is divisible by 6 Read More »
Prove That the Product of Three Consecutive Positive Integers Is Divisible by 6 Video Explanation Question Prove that the product of three consecutive positive integers is divisible by 6. Solution Step 1: Let the Three Integers Be Let the first positive integer be \(n\), where \(n\) is a positive integer. Then the next two consecutive
Prove that the product of three consecutive positive integers is divisible by 6 Read More »
Prove That the Product of Two Consecutive Positive Integers Is Divisible by 2 Video Explanation Question Prove that the product of two consecutive positive integers is divisible by 2. Solution Step 1: Let the Two Consecutive Positive Integers Be Let the first positive integer be \(n\), where \(n\) is a positive integer. Then the next
Prove that the product of two consecutive positive integers is divisible by 2 Read More »
Prove That One of (a+b)/2 and (a−b)/2 Is Odd and the Other Is Even Video Explanation Question If a and b are two odd positive integers such that a > b, prove that one of the two numbers \(\frac{a+b}{2}\) and \(\frac{a-b}{2}\) is odd and the other is even. Solution Step 1: Express Odd Integers in
अमेरिकी सरकार का शटडाउन (Government Shutdown) 2025 में 1 अक्टूबर से शुरू हो गया है। इसका कारण कांग्रेस में रिपब्लिकन और डेमोक्रेटिक नेताओं के बीच फंडिंग बिल पर सहमति न बन पाना है। इससे सरकारी सेवाएं और कई कार्यक्रम अस्थायी रूप से बंद हो गए हैं और लाखों सरकारी कर्मचारी अवैतनिक अवकाश पर हैं। ट्रंप
सम्राट चौधरी बायोग्राफी: बिहार के उपमुख्यमंत्री सम्राट चौधरी (जन्म— 16 नवम्बर 1968; लखनपुर, मुंगेर, बिहार) भारत के प्रमुख राजनेता और वर्तमान में बिहार के उपमुख्यमंत्री हैं। वे भारतीय जनता पार्टी (BJP) के प्रमुख नेता, जातीय राजनीति के माहिर खिलाड़ी और कुशवाहा समुदाय के सम्मानित चिह्न हैं।prabhatkhabar+1 प्रारंभिक जीवन और शिक्षा जन्म: 16 नवम्बर 1968, लखनपुर,
Class 11th Maths – RD Sharma Chapter 2 : Relation Exercise 2.1 Solutions If (a/3 + 1, b – 2/3 ) = (5/3, 1/3) find the value of a and b. Watch Solution If (x+1, 1) = (3, y-2), find the value of x and y. Watch Solution If the ordered pairs (x, -1)and (5, y)