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Suppose to the contrary that this equation had an integral solution.Let’s reduce this equation modulo 16:[math]x^4 + y^4 + z^4 - w^4 \equiv 11 \bmod 16. \tag*{}[/math]However, it is easy to verify that the fourth powers of even and odd integers are congruent to 0 and 1, respectively. In particular, this implies that [math]x^4 + y^4 + z^4 - w^4 \not\equiv 11 \bmod 16[/math], giving us a contradiction.

One of Euler's sum of powers conjectures. In particular, Euler claimed in the 18th century that there were no whole number solutions for the following equation:[math] x^4 + y^4 + z^4 = w^4 [/math].It wasn't until 1988 that Harvard professor Noam Elkies (Noam D. Elkies Home Page) found a solution:[math]2682440^4 + 15365639^4 + 18796760^4 [/math] = [math]20615673^4[/math]He also proved that infinitely many solutions existed to the equation. What's incredible about this is that for over 200 years nobody could neither prove nor disprove the conjecture.Source: The Whole Story

Red SkullWe saw this showdown before, but this time, Captain America is more experienced. Red Skull is dead, again.W-1: L-0Yon RoggNormally Captain America would win, but Yon Rogg has a gravity gun, so I don't think Cap would be able to touch him.W-1: L-1Iron MongerAll Iron Monger needs to do is fly into the air and shoot Captain America on the ground.W-1: L-2WhiplashWhiplash could just use one whip to try and get his sheild, the other whip to get Captain America, then Cap is done.W-1: L-3AbominationCaptain America isn't strong enough or fast enough to go against Abomination, he'll die trying.W-1: L-4LokiHe's the God of mischeif, Captain America won't be able to tell what's real and what's fake before he's killed.W-1: L-5Aldrich KillainIn hand to hand combat, I don't think Captain America can handle all the burns he’s going to get when fighting him.W-1: L-6MalekithThis guy knows some magic, which won't be good for Captain America.W-1: L-7Winter SoldierWe’ve seen this before, only Captain America is better experienced this time, so Bucky fails.W-2: L-7RonanThis guy is stronger than Captain America and knows hand to hand combat, so Ronan would win this one.W-2: L-8EgoHe's a planet, end of fight.W-2: L-9UltronUltron almost defeated Thor, Captain America should be easier than that.W-2: L-10YellowjacketEven normal sized, Captain America will likely dodge his stingers and defeat him.W-3: L-10ZemoThis guy is just a guy, so Captain America can beat him without breaking a sweat.W-4: L-10KilmongerHe has the same strength and speed of Captain America, and has a vibranium suit, so Cap wouldn't win this.W-4: L-11VultureHe is too big and to fast for Captain America to defeat.W-4: L-12DormammuHe is a multerversal being, Cap is dead.W-4: L-13HelaThor and Valkyrie couldn't even defeat her, Captain America would be a joke to her.W-4: L-14GhostCaptain America is too fast for her to catch, and she needs to come out of phasing at some point, Cap could take her down then.W-5: L-14MysterioCaptain America wouldn't be able to tell what's real and what's fake, he's dead.W-5: L-15ThanosWe already saw this, and it would turn out exactly the same.W-5: L-162014 ThanosThis guy beat Captain America twice, and he'd do it a third time if he had the chance.W-5: L-17So Captain America wouldn’t do so good outside of the villains he fought in his movies.