Consider the following multiplications. . Also . Try also several calculations like these and observe what happens. From these calculations, we can observe that and or, in general . We now, prove our conjecture. Theorem: Proof If we multiply the expression on the left hand side by itself n times, we have . On the […]

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# Algebra

## Difference of 3-Digit Numbers with Reversed Digits

In the previous post, we proved a theorem that the sum of a 2-digit number with reversed digit is divisible by 11. In this post, we will learn another theorem about numbers with reversed digits. This time, we will explore the difference between two 3-digit numbers with reversed digits. Let’s have the following examples. 231 […]

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## The Sum of Two 2-Digit Numbers with Reversed Digits

Let us observe the sum of a 2-digit number and a number formed by reversing its digits. 23 + 32 = 55 63 + 36 = 99 43 + 34 = 77 21 + 12 = 33 26 + 62 = 88. Notice that all the numbers are divisible by 11. Now, are all such […]

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