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Whereas a list of the possible x-values can be established by a brute-force search, this is not possible for the y-values. Some, however, may easily be excluded. For example, 4 cannot occur in this sequence, since for even y, x must be odd, and for x = 2k - 1, x^4 + 4^x = (x^2 + 2^k*x + 2^x)(x^2 - 2^k*x + 2^x).