This is just about completely incorrect. The M was developed from a Republic test mule in 1943 for the C series engine. It was built specifically to chase down V-1s. The N was engineered specifically for the Pacific.
I can into this in more detail, but I suggest that you do some basic research on the web rather than me spending more time correcting your post.
My info comes from Republic design notes and mission goal of the M, Sir! As the war progressed, the wing on the M would not be large enough for the long flights to and from Japan, so there fore, they redesigned the wing, extending the fuselage and called it the N model. The M saw some service in the European theater, but because of ignition problems and other engine problems, never did carry out its goal of shooting down V bombs. It did get 15 kills, late in the war. The N did turn out to be a good aircraft for air to ground attack roles, but because of the additional weight over the M, never was a good, fighter aircraft.
This is, I guess, where you got your info:
Throughout the war, the P-47 would undergo constant development. A bubble canopy was added to increase backward visibility.[6] The final version of the P-47 would be the P-47N, a long-range version with longer wings and fuselage, and an increased fuel capacity. The P-47N was designed to escort B-29s on long missions to Japan for a planned invasion of the Japanese homeland that never came. Production of all versions ended in November 1945. By then, 15,660 P-47s had been built, making it the most produced U.S. fighter of the war. 1,816 would be the long range P-47N model. This model would continue to serve with Air Force Reserve and Air National Guard units until the mid-1950s.[7][8] Republic ranked 24th among United States corporations in the value of wartime production contracts.[9]
In late 43, it was common knowledge, or most experts felt, the U.S. would have to invade Japan and would need long range fighters to escort the bombers to Japan! Republic brass thought that there would be a large contract for this type of aircraft, hence the M was developed and as time and events occurred, it was decided to improve the M with the new wing and extend fuselage, hence the N was born. Trouble was the N was needed more in Europe against German tanks, there fore it was rushed in to production and was successful in that role.
A quote from the "Jug" Assn about the jug during WW2:Thunderbolt pilots claimed to have destroyed 86,000 railroad cars, 9,000 locomotives, 6,000 armored fighting vehicles, and 68,000 trucks, all in Europe.
But to put a end to this long winded reply to your post, the Jug series of aircraft served in all theaters of operations thoughout the world, except Alaska.