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Solution
$$37^{57}+43^{57}=\left(37+43\right)\left(37^{57}-37^{56}.43^1+37^{55}.43^2-37^{54}.43^3+.....+43^{57}\right)$$
$$37^{37}+43^{37}=\left(37+43\right)\left(37^{37}-37^{36}.43^1+37^{35}.43^2-37^{34}.43^3+.....+43^{37}\right)$$
$$\therefore$$The common factor of $$\left(37^{57}+43^{57}\right)$$ and $$\left(37^{37}+43^{37}\right)$$ is $$(43+37)$$
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