prove by induction that 6^n-1 is divisible by 5?
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Proving 6n−1 is always divisible by 5 by induction Prove 6n−1 is always divisible by 5 for n≥1. ... Base Case: n=1: 61−1=5, which is divisible by 5 so TRUE. Assume true for n=k, where k≥1: 6k−1=5P.
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The answer is 6(six). its 6 . because 5+1 = 6. 1 more than 5 is 6.
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3, 6, 9, 12, 15,18, 21, 24, 27, 30, 33, 36, 39, 42, 45, 48, 51, 54, 57, 60, 63, 66, 69, 72, 75, 78, 81, 84, 87, 90, 93,96,99 are divisible by 3.
308391
A number is divisible by 6 if it is divisible by 2 and 3 both. Consider the following numbers which are divisible by 6, using the test of divisibility by 6: 42, 144, 180, 258, 156. [We know the rules of divisibility by 2, if the unit's place of the number is either 0 or multiple of 2]. 42 is divisible by 2.
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Answer. Let P(n): n(n + 1)(n + 5) is a multiple of 3. For n = 1, the given expression becomes (1 × 2 × 6) = 12, which is a multiple of 3. ... Hence, by the principle of mathematical induction, P(n) is true for all n ∈ N.
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['Any integer (not a fraction) is divisible by 1.', 'The last digit is even (0,2,4,6,8) ... ', 'The sum of the digits is divisible by 3. ... ', 'The last 2 digits are divisible by 4. ... ', 'The last digit is 0 or 5. ... ', 'Is even and is divisible by 3 (it passes both the 2 rule and 3 rule above)']
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If 4^n-1 is divisible by 3, it can be written as 4^n -1 = 3*k, where k is an integer. 4^(n+1) -1 = 4 * 4^n -1 = 4 * (4^n -1 + 1) -1.
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Therefore, the answer to what divided by 6 equals 4 is 24. You can prove this by taking 24 and dividing it by 6, and you will see that the answer is 4. Tip: For future reference, when you are presented with a problem like "What divided by 6 equals 4?", all you have to do is multiply the two known numbers together.
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P(k): 23k – 1 is divisible by 7. ... = 7(8m + 1), which is divisible by 7. Thus, P(k + 1) is true whenever P(k) is true. So, by the principle of mathematical induction P(n) is true for all natural numbers n.
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(4 + 6 + 1) - (2 + 5 + 4) = 0, So, 415624 is divisible by 11.
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We need to answer if m is divisible by 6. The answer has to be a definitive YES or a NO. The test of divisibility for 6 is that the number should be divisible by both 3 and 2.
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Thank you. n(n^2-1 ) is always divisible by 24 for all odd numbers..
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Given : 871*45 is divisible by 9 & 534*0 divisible by 18.
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A number is divisible by 5 if the number's last digit is either 0 or 5. Divisibility by 5 - examples: The numbers 105, 275, 315, 420, 945, 760 can be divided by 5 evenly.
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To check, replace x with 5 such that x + 6 = 11. Then, 5 + 6 = 11. Thus, 11 = 11.
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All numbers divisible by 4 are divisible by 2 . But all numbers divisible by 2 are not divisible by 4.
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Thus, the answer to "5 divided by what equals 5?" is 1.