Use induction to prove that (5^{2 n}-4^{n}) is divisible by 7 for all natural numbers (n).

Question:

Use induction to prove that $5^{2 n}-4^{n}$ is divisible by 7 for all natural numbers $n$.

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For answer-question

Calculus

ISBN: 9781319055844

4th Edition

Authors: Jon Rogawski, Colin Adams, Robert Franzosa

See More Books

Question Posted: Jan 28, 2024 12:02 AM

See More Questions

On December 1, 2016, Insto Photo Company purchased merchandise, invoice price $25,000, and issued a 12%, 120-day note to Ringo Chemicals Company. Insto uses the calendar year as its fiscal year and...
Write a critical essay focusing on the issue of "Gender Violence" Assignment guideline: Locate a case of "Gender Violence" from Bangladesh regarding Sex and gender, recurrent gender patterns, economy...
Rand Medical manufactures lithotripters. Lithotripsy uses shock waves instead of surgery to eliminate kidney stones. Physicians' Leasing purchased a lithotripter from Rand for $2,000,000 and leased...
A wheel 33 cm in diameter accelerates uniformly from 240 rpm to 360 rpm in 6.5s. How far will a point on the edge of the wheel have traveled in this time?
Timmins Grow-Fast spreads herbicides and applies liquid fertilizer for local farmers. On May 31, 2020, the companys Cash account per its general ledger showed a balance of 6,738.90. The bank...
Panther Racing, LLC, is involved in competitive racing, including the development, maintenance, and operation of a racing team in the IndyCar series. Beginning in 2008, the National Guard annually...
Teri Hall has recently opened Sheer Elegance, Inc., a store specializing in fashionable stockings. Ms. Hall has just completed a course in managerial accounting, and she believes that she can apply...
4. Consider the tables of values for the two functions shown. x y = f(x) -2 5 y = g(x) -2 -1 6 -1 0 8 1 1 7 0 2 9 2 Complete the table of values for the composite function y = f(g(x)). - x y =...
Use Pascal's Triangle to write out the expansions of $(a+b)^{6}$ and $(a-b)^{4}$
Use induction to prove that $n^{3}-n$ is divisible by 3 for all natural numbers $n$.
When would you expect cyclical unemployment to be rising? Falling?
Calculate the power a car engine contributes to speeding the 2100 kg car up to a highway speed of 65.0 mi/h in 13.0 s.
1. XYZ is considering a project with the following data: Sales Revenue = $500,000 Pre-tax Cannibalization cost = $50,000 Asset Cost = $450,000 Straight line depreciation over 3 years with zero...
Chandler purchased his home in 2010 and his cottage in 2012. In 2014, he disposed of both the home and the cottage. The home has a capital gain of $75,000, whereas the cottage has a capital gain of...
Yesterday, Tessie T s Corporation purchased (and received) raw materials on credit from its supplier. All else equal, if Tessie T s current ratio was 2.0 before the purchase, what effect did this...
3. A city has 200 white households and 100 black households. It has 3 neighborhoods. The first neighborhood has 100 white households and 20 black households. The second neigh- borhood has 50 white...
What factors should a company consider in estimating the useful life of an intangible?
On March 31, 2018, Gardner Corporation received authorization to issue $30,000 of 9 percent, 30-year bonds payable. The bonds pay interest on March 31 and September 30. The entire issue was dated...
Determine whether the series converges or diverges. e" + 1 -1 " + 1 00
Determine whether the series converges or diverges. 1 -2 ? 1
Determine whether the series converges or diverges. 2 1 - -n n=1
Select all that apply Net income attributable to noncontrolling interests will be a reduction in arriving at net income attributable to controlling shareholders. is an expense in the consolidated...
Select all that apply Minority-passive equity investments generally Multiple select question. are accounted for at present value of future cash flows. have changes in present value accounted for in...
Apply Minority-passive equity investments generally. are accounted for at present value of future cash flows. have changes in present value accounted for in other comprehensive income. have changes...

Use induction to prove that (5^{2 n}-4^{n}) is divisible by 7 for all natural numbers (n).

Question:

Step by Step Answer:

Calculus

Students also viewed these Mathematics questions